If you're a thief then go to a wiki and look up the 'Stones of Barenziah' quests. Speaking from personal experience, they're time-consuming but worth it.

As another poster mentioned, the invisible perk you get as a reward greatly increases the number of gems you find in loot.

It doesn't take long before you have more than you can even sell in one visit to the fully upgraded Riverwood merchant.

Steps to be super rich in Skyrim:

1. Go full alchemy.
2. Make potions of fortify health, slow, damage magicka and stam regen,etc.
3. Drink haggle potions.
4. ???????
5. Profit

alchemy is a cash farm, I mix ingredients that have fortify and resist/weakness and get potions well over 350 coins (or poisons, for some reason all effects count to value no matter what effects, (like fortify magic, drain health would be 300ish))