What is the fastest way to earn coin?

Chop wood and sell it.

Anything else?

Radiant Quests for the Companions, Thieves Guild, or Dark Brotherhood can net you a pretty penny..

Or, just go raid a cave with alot of Bandits, strip em nvde and sell all their Armor and Weapons..

Khajiit chest in Dawnstar. If you wait until the caravan is at Dawnstar, you can reset the chest contents using the vender reset method: save, assault vender, reload save, open vender inventory (what do you have for sale), close it, loot chest. Repeat. The chest contains 750 coins, plus lots of loot that can be sold to Dawnstar vendors. You can use the same vendor reset on the local venders to replenish their cash as they run out. Easy 4000-5000 each time you loot the chest and sell. And you never have to leave Dawnstar.

If your stats are high enough, use the resto-loop to make expensive potions and sell them.

Become a regular alchemist and take the perk that lets you sell anything to any vendor. Even without the resto-loop method, you can make bucket loads of potions (some quite pricey) and sell them to any vendor.

Otherwise, it is the normal way as noted by others above. Bring a follower so you can carry everything out of a dungeon/cave. You can get your follower to exceed their carry weight limit by using the point method to tell them to pick up stuff from the floor. Leave nothing behind. Books, cups, treasure, weapons, armor, etc. It all sells!

Doing favors and side quests. Just venturing out in the open world and dont think about it too much. The coin will come.

Banish enchantments, from what i can tell they seem to be the highest value you can slap on a weapon. I usually do it to raise enchantment, but after a while you'll make weapons worth more than most vendors can afford. At low levels the transmutation spell to make gold jewelry works well. If you don't mind an exploit you can buy all the cheap ingredients from an alchemist, turn them into potions, save, punch the alchemist and reload to sell your potions, repeat until bored.