1) Get souls.
2) Make enchanted iron daggers.
3) Sell them.
4) Repeat.
1) Getting souls: This is stupid easy if you're a caster, just learn and use soul trap. If you're a weapon user, you'll need to obtain and learn the soul trap enchant. Keep an eye out when you hit weapon vendors for the enchant. On my latest playthrough, I was able to buy one when I got back from clearing out Bleak Falls Barrow. Obviously, you'll need a good stockpile of soul gems to contain all the souls you'll be reaping. The hardest part will actually be carrying enough petty soul gems to protect your better gems. Hit every general goods vendor and court wizard you can find, and snap up every empty petty gem you can find. You'll use them.
2) Make enchanted iron daggers: Don't dig iron ore, don't carry a pick. You're an adventurer, not some lowly mine-lackey. Seriously, toting around the massive ten pound pick isn't worth the trouble, because iron ore is cheap! So are the ingots. Buy them off the three blacksmithing vendors in whiterun, and then use the leather you've probably gotten by accident already to craft a pile of iron daggers. Your smithing skill will rise, good for improving your gear as the game progresses, but more importantly, you'll also have grist for your soul gems. What enchant to use? Just pick the one that sells for the most! Keep an eye out for weapons of Banish, that's the cash-cow enchant, but others will serve just fine until you get there.
3) Sell them: You don't need help with this part, right? Well, some things to watch out for: An amulet of Dibella should be easy to find and will get you a price break on buying materials and selling finished goods. Also, convenient for bluffing your way into Riften, where you can join the thieves' guild. The hat from their armor gives another 10% break on your prices. And of course, don't forget that you can sell your finished daggers to five different vendors in town: Eorlund Greymane, Belethor, Elrindir in the Drunken Huntsman, and Ulfberth War-Bear and Adrienne Avanicci in Warmaiden's. Between them you can unload nearly 5000 gold worth of inventory per day, more if you buy raw materials off them, like iron, soul gems and leather.
4) Repeat: As I said earlier, the only challenge in this method of earning money is keeping your stockpile of soul gems up, particularly petty gems. Later, once you get a bit tougher, head up to the Shrine of Azura and finish the quest to get either Azura's Star or the Black Star. The Black Star is best if you're not a conjurer, as Grand White Souls can be hard to come by. If you're heavy in Conjuration, you can summon Atronachs and slay them to fill your Azura's Star instead.
Worst case, an iron dagger will cost 66 gold to make, and even the lowly fire enchant will sell for over 200 gold. Your margins will steadily improve as your speech and enchanting skills rise, and as you learn more profitable enchants.
