Early game and for small sums, stealing everything in sight and selling to the Thieves Guild fence is decent. Thieves Guild can be found in Riften, talk to the people in the market. Once you complete a quest or two you can use the fence.
Raising your Speech
Picking up and selling everything you can helps. But if you just want to level up Speech quickly to get a better margin on what you sell, go into the Meadery in Riften, and talk to the guy behind the counter. Ask him about Maven and you'll get a chance to do a Persuasion check. You can ask him that same topic repeatedly, increasing Speech each time. It really isn't necessary to put perks into Speech as you can make a ton of money.
Improve your barter
There are a few ways to improve barter besides your Speech. An altar of Zenithar will give you +10% for 7 hours. You can find one if you go to the Riften stable, head down the hill, and turn right after the 2nd watch tower, going up the hill along the tiny dirt path. There is a critter up there the first time you go. You'll find the altar, and also can pick up an Amulet of Zenithar that also gives a 10% bonus. So between the two you've got a 20% bonus, you just need to equip it when selling, and check your Active Effects in the magic menu every once in awhile to make sure you don't need to go refresh it. Also realize any other altar you pray at will replace it.
Another way you can improve your Barter is to complete the beginning of the Thieves Guild and wear the hood that they give you when selling things. It's a +10%, so with the two above you're up to +30% on prices.
Pickpocket trainers
If you are training your stats, a lot of your money in the game goes to trainers. You can steal the money back from them, essentially training for free. The more money, the harder it is to steal back, so you may need to train once, steal it back immediately, repeat. Also, if you go this route, your will level super fast as Pickpocket increases quickly when stealing the amounts of coin you spend for trainers. You can also just pickpocket normal people, there are a lot of people with jewelry that will sell for 75-100.
Enchant
Enchanting weapons is incredibly easy to make money. It's like having your own printing press. First you'll need to disenchant some weapons to learn the enchantment you'll put on it. Banish (banishing Daedra) is the best but weapons won't show up with it until you're higher level. Paralyze is next best, followed by Absorb Health. Early game, Turn Undead and Damage Stamina are the two that you are most likely to find weapons with. The money for weapons is much, much higher than that for armor, so don't bother trying to enchant armor unless you plan to use it.
To churn out weapons, head up to the mage college in Winterhold and buy up all the Petty soul gems you can, including those that have souls. Buy the Soul Trap spell and head out into the wild. Every time you come across a critter, hit him with a Soul Trap spell before killing him. You have to be in touching range. You can also use a weapon with Soul Trap on it, though you have 60 seconds to kill it with the spell, only a few seconds with a weapon.
I normally enchant whatever weapons I find in my travels, but if you don't have weapons to put the enchantment on, just head to any blacksmith and buy up their iron ore, and also some leather strips or leather. The ore is much cheaper than ingots, and you can smelt it into ingots at most of the blacksmiths, including whiterun where it's kind of set back behind the building and forge a little. Turn them into iron daggers at a forge and then enchant the daggers. You won't make money off of just making the daggers and selling them, but with the enchantment you'll make enough even starting out with Damage Stamina that you can afford to buy ore and a soul gem with a Petty or Lesser soul already in it, and still make money. The enchantment adds the same amount of money regardless of weapon type, so you won't make any more by making a sword instead of a dagger. The dagger requires the least amount of materials, so is the best to do. It's very easy to just run around and kill wolves and such to fill up gems.
Right now I have about 20k in coins and I probably have 30 weapons sitting in a chest I haven't bothered to sell yet, with a 1k or more selling price at 50 speech... made with 100 enchant, dual enchanted with Banish and Paralyze.
Potions
Another easy way to make money, though in lesser amounts than Enchant, is by making potions. Every time you go through a town with an alchemy shop, stop in and buy all the ingredients that are low price. Starting out I buy anything that costs 10 coins or less. As my alchemy goes up and I start making more money for potions I buy higher and higher priced ingredients. I generally dump them all in a chest in my Whiterun house and then when I've accumulated a lot, go potion crazy.