Not until level 70-- You don't want to farm items which will someday be obsolete. Also, wait until you can do around 40k damage. Before that, you just can't move through levels fast enough to make farming worth it. You can get by with jewelry crafted with rough gems or no gems at all for a while.
The goal here is to move quickly. Find a level with a lot of densely-packed enemies or an easy to reach boss, and kill as fast as you can. Remember that short levels mean more down-time in the loading and end screens, while long levels mean more time walking and fewer bosses. Play on a difficulty level where you can't die, no matter how many enemies attack you at once, and attract as many enemies as you can at a time. Put your champion levels into movement, and grab a few +movement items. They make a big difference. For mages, Lightning is your spell of choice. It kills multiple enemies at once, can go through walls, has a very long range, and increases your movement speed. You won't have to chase down enemies with Lightning. Vortex can be useful too, since it pulls groups of enemies together and stuns them. Never stop to collect drops. They'll all fly at you at the end of the level. Ignore groups of enemies and even chests that are out of the way. When you're farming, you can't waste thirty seconds chasing after a small chest!
If you want the best items, focus on bosses. If you want the most gemstones, focus on large groups of normal enemies.
The Siege of Anderhelm (level 11) This one's my favorite. It has one boss and a boss chest, it's almost as short as the Severed Mountain, and and the enemy density is very high for plenty of gemstones. Go straight through with Lightning, attracting several groups of enemies at once. Don't bother with side passages and small chests, since they'll just slow you down, but if you swerve back and forth a little, you'll be able to hit a few extra enemy groups without adding too much time. Ignore the towers, and go straight to the boss. After you kill him, wait a second -- you'll fire one lightning bolt to either side to kill nearby enemies, so if you don't wait, you'll have to chase down enemies. After that, grab the chest, and you have just enough time to clear one of the towers while the level's rewards fly at you.
My results: I had 19.2 movement, 64k damage, 2000 life on hit, around 90 champion levels, and no +gold%. In 13.5 minutes, I got 26k gold, 4 gems, and the equivalent of 44 rough gemstones. Per minute, that's 1900 gold, 0.3 gems, and 3.2 gemstones. Keep in mind that there's a ton of variability. I'd need to test it for a couple hours to get more accurate numbers.
The Severed Mountain (level 10) This level is very straightforward, and has the easiest to reach boss in the game, making it good for gem and set farming. With enough +movement, you can skip all the normal enemies, kill the boss, and abandon the level. Alternatively, you can quickly kill the normal enemies to get gemstones and gold. The strategy is to move past one group of enemies so you can get two groups at a time with your lightning. Take one path on the circle at the end, kill the boss, and kill the final group on the other side of the circle while everything's flying at you.
My results: I had 19.2 movement, 64k damage, 2000 life on hit, 100 champion levels, and no +gold%. In 11.5 minutes, I got 25k gold, 9 gems, and the equivalent of 18 rough gemstones. Per minute, that's 2200 gold, 0.78 gems, and 1.5 gemstones. Keep in mind that there's a ton of variability. I'd need to test it for a couple hours to get more accurate numbers.
In this thread, heliax2112 points out a way to get even more gemstones from this level. If you use your abilities to stun Margoth for long enough, you can kill him before he runs away, resulting in a 100% chance of a gemstone drop. I haven't done a direct comparison, but that extra drop might make this a better farming level than the Siege of Anderhelm.
The City of Malador (level 39) This is one of the longest levels in the game. It has a ton of large groups of enemies, a boss who spawns more enemies, three boss chests, and maybe 10 small chests which aren't that out of the way. Focus on +movement because you're going to spend a lot of time walking. This level will get you lots of gemstones and gold, and since it's long, you won't have to spend so much time on the start screen.
My results: In six minutes on Normal, with champion levels put into movement speed but no +movement items, I can do one run, and I usually get about 5 gems, 1-2 purples, enough blues and greens to almost fill my 4 rows of inventory, and a ton of gold. I have not done any real timing for this level.
Other levels of note The Broken Dragon (level 16) is too long with too few enemy groups to be worth farming.
The Temple (level 29) has a ton of enemies and chests, plus a boss, making it good for gold and item farming.
The Crucible of Mawrth (level 40) is also very long, but has some nice groups of elite enemies. The final boss of the game is in this level, so I would guess that he gives some nice drops, but I haven't tested it.
A Note on Buying Gemstones Gems are the game's super-currency which you can buy for real money or find during your adventures, and 99 gems can be used to buy a gemstone packs. How many gemstones is a gem worth? Averaging 10 gemstone packs, I've gotten the equivalent of 238 rough gemstones from each. That's 2.4 gemstones per gem. What this means is that, while gems help, you're going to get a lot more gemstones through drops than from the store.
There's a deal in the store where you can get 100 gems a day for 30 days, for $4 US. Those 3000 gems are worth 7200 gemstones.
Casual Farming What if you don't play any levels at all? Let's take a quick look at the Reward Calendar. This month, I see 310 gems and 3 bags of gemstones. 310 gems at 2.4 gemstones per gem makes 744 gemstones, and 3 bags at 238 each makes 714. That's 1458 total. So to get a single perfect piece of jewelry would take one year of passive farming.
Okay, so what if you just do Gorgana three times a day, and maybe one level here and there for daily rewards that Gorgana doesn't complete? A Gorgana level gets you about 2 gemstones and 1 gem, the daily reward is worth 20 gems, and the occasional level gets you, say, 1 gem and 3 gemstones a day. That's a total of 9 gemstones and 24 gems a day, or 270 gemstones and 720 gems a month. Added to the Reward Calendar, you're up to 1199 gemstones, and 1030 gems which are worth 2,472 more. At that rate, it will take about 5.3 months to get a piece of perfect jewelry.
Of course, if you're a casual player, you're not going to expect perfect jewelry. Go for level 4 gems and you get two nice rings in less than two months. Level 5 gems will get you all three pieces of jewelry in 5.3 months, and that's pretty close to perfect.
Watching Videos Once or twice a level, you have the option of watching a 30 second video for five gems. Is it worth it? 5 gems is the equivalent of 12 gemstones, which is nearly twice as many as you can get in 30 seconds of farming, so yes, it's worth it. There will be a cut-off point -- some movement speed + damage combination where the videos are no longer worth it -- but it's at a very high champion level. Now you just have to figure out for yourself whether it's worth interrupting your game-play to double your farming speed.
How long does it take? Farming takes patience. It takes many boss kills to get a single useful gold or set item, and it takes forever to collect gemstones. The top gemstone is the equivalent of 243 rough stones. To make a single perfect ring (with each level socketed with perfect stones), you need 40 perfect stones, which is the equivalent of 9,720 rough stones, and since you probably don't want to use half your gemstone colors, you really need twice that, or 19,440. Taking my numbers from the Siege of Anderhelm, I get the equivalent of 3.2 gemstones per minute, plus 0.3 gems, which translates to 0.72 more gemstones. That means it would take me 80 hours to get enough stones to craft a single perfect ring, and that's just one of the three pieces of jewelry you can carry!
Lowering your standards helps a lot. Each step down in gemstone quality reduces your farming time by 2/3, so Trillion (level 5) stones will get you a ring in 27 hours, and Radiant (level 4) will take 9 hours. Teardrop (level 3) is ideal for casual players, requiring only 3 hours per item of jewelry.
Since you're not going to do an 80 hour marathon session, let's see what this translates to in real time. Let's say you put in an hour a day. 10 minutes of that are going after Gorgana, leaving 25 hours of farming a month. Gorgana will get you 180 gemstones and 90 gems a month, and regular farming will add 4,800 gemstones and 450 gems. You also get 729 gemstones and 310 gems from the Reward Calendar, and 600 gems from daily quests. In total, that's 5,709 gemstones and 1,450 gems, which comes out to the equivalent of 9189 gemstones a month. So a two months of serious farming will get you one perfect piece of jewelry, or all three pieces slotted with level 5 gemstones.
Throw in the 100 daily gems deal for $4 US and you're up to 16,390 gemstones a month, which is twice as fast. This deal becomes more valuable the less you play.
If your goal is gold, you want the highest difficulty level you can run through quickly. One level stands out at all difficulties. Go to The City of Malador (level 39). Get to the boss as fast as you can with +movement items. At this point, you want enough toughness that the boss can't kill you easily, low enough damage that you can't kill him easily, and +gold% if you can fit it in. Now run around teasing the boss until he spawns lizards. Each time you kill the lizards, you'll get several question-mark boxes full of gold. You can farm these little guys as long as you want, collecting huge amounts of gold. Just hope the game doesn't crash before you finish the level! Avoid stunning or freezing the boss, because he'll spawn fewer lizards.
When farming gold (or XP) on other levels, know that +gold% is a good item choice, but not always the best. If you have +100% gold, but it takes you twice as long to finish levels, you're getting the exact same amount of gold, but half as much XP, and half as many gems and items. You're better off carrying around some good +gold/XP% jewelry, and equipping them at the end of the level before everything you missed flies at you. Also keep diminishing returns in mind. Going from +0% to +30% gold makes a big difference. Going from 200% to 230% doesn't matter nearly as much, since that's only a net difference of 10% (trust me -- I don't feel like explaining the math right now). So your first +gold item might be better than your tenth +attack speed item, but your tenth +gold item isn't worth much at all.
This one's tough. Gorgana's a good place to do this, but you only get 3 keys a day, and she takes a long time to kill. So as not to waste time, fight her on a difficulty level where you can kill her fairly easily. For me at champion level 100, that's still Normal.
Once you've used up your keys, just kill bosses as fast as you can. The easiest bosses to get to are in The Severed Mountain (level 10) and The Siege of Anderhelm (level 11). Do this at the highest difficulty that you can complete in a reasonable amount of time.
I got these methods from Mukraise. With both of these, you want to max out your +experience% gear. Mukraise does 60k dps, and puts other gear into armor and vitality.
The AFK method In level 24, the Scent of Home, you can shoot the first enemy, and you'll often just keep shooting until the level is over. As long as you're paying just a little attention, your level (and gold, gems and gemstones) will go up with very little work on your part.
The Speed Grind Method Level 20, Canyon of Whispers, takes full concentration. According to Mukraise, it's the fastest way to level in the game. Using plenty of +movement equipment, do the level until you get to the first circle ring on the map, where mobs spawn. Then abandon and restart.
It is good to start as soon as you unlock your trials. Just advance through the trial levels in order to get basic loot to be able compete with monsters in the Story mode.
If you are willing to become one of those endgame players that move around big trial numbers, you will need proper gear and advanced number of champion points. So, there's no mistake to play AFK based story levels or loot some experience in Canyon of Whispers.
This time, you don't need to hurry anywhere. The rewards are the same and aren't based by time.
Never forget that Bosses rewards can be sold for gold, so even epic items are worth it to obtain. You can also focus on clearing faster, it is better to go for lower level trials if it takes you long when covering on the high ones. But if you are able to fastly clear trials over 100, then take an advantage of that.