Design: Veiled Noble Topaz - Every caster needs these
Design: Royal Nightseye - Amazing healer gem
Design: Solid Star of Elune - Tanks cry for these 24/7
Design: Runed Living Ruby - Another caster gem, very high demand.
Keep an eye out for these patterns all the time. Everytime I am in a major city, I check the AH for ALL rare JC recipes. You will sometimes get recipes for insanely cheap (I got solid star of elune, a 1k gold pattern, for 250... and I got veiled noble for 6g).
Now that you have the patterns, where do you get the gems?
Well, there's two ways. One is to buy the gems off the AH, cut it, and repost. This has little to no risk (it might not sell), and will almost ALWAYS yeild profit of 5-10g.
The other, and the way you will make insane amounts of gold, is through prospecting. Prices vary from server to server, but on my current server, a stack of Adamantite sells for 20g. Figure out what the average price is on your server, and buy anything under average (even if by a couple gold). Prospect it all.
From my tests, each stack has an 80% chance to yeild a rare gem. You spend 20g for a stack, and 20% of the time you will get no gem. But, that means that 20% of the time you will get two, or even three rare gems. ANY in-demand gem (even Talasites) will sell cut for over 20g on my server, which means you have an 80% chance to make money per stack.
But wait, if you're spending 20g on a stack, and the gems are selling for 20g, how is that profit?
Adamantite Powder and Green Gems. After a while you will end up with stacks of 20 uncommon gems, you can post these on the AH easily for 20g a stack. People who want to power level JC will buy them all.
Adamantite Powder makes Prospecting EXTREMELY profitable, and most people do not realize this. I have talked to some of the biggest JC whores on my server only to find out that they vendor their powder. I didn't let them in on my "secret", but I will tell you.
Find yourself a nice, cheap ring pattern. I used :
Design: Delicate Eternium Ring
These things sell for 50g easily. Now lets do the math.
100 adamantite ore (5 stacks) = 100g
Prospect it all, you end up with 20 adamantite powder (1 stack).
Make the powder into mercurial
(4x powder and 1x primal earth, any Miner will have thousands of these), and you end up with 5 mercurial.
Buy an Eternium Bar from the AH (5g) and make the ring.
Out of that 100g, you just made 50g back. That means you paid 50g for 5 stacks of adamantite, or 10g a stack.
So you're paying 10g for an 80% chance at a rare gem that will DOUBLE your gold (cheapest a gem goes for is 20g cut), you have a chance of getting gems which easily sell for over 50g (living ruby), and you have a chance at getting 4 gems.
For the TL;DR people:
Cut into popular gems
Make powder into rings
Get a much better guide by following the link below