Once you get a broker and a bookkeeper, or a manager and a bookkeeper (don't remember which), the economy starts up. These dwarves are nobles (purple), so their presents represents your official inclusion in the larger dwarven system. The bookkeeper doesn't come until you have some coins (a bookkeeper also lets you count all of our items and zoom to any item). Once the economy has started, non-noble dwarves have wages and must pay rent. They can also buy and sell things in stores that you set up. The stores are run by the broker/bookkeeper at first, but any enterprising dwarf can buy in to one. The stores are stocked by goods that the dwarves make. It would be too messy to have them all bring their goods to market and waste time selling them, so instead, they are paid for producing the good, which becomes state property. The store owners can buy state property at a discount, and then sell it at whatever price they like, and keep the profits. It's kind of strange, but since the laborers didn't pay for the materials they are using in the first place, it makes sense in a way for things to revert to state ownership, provided the laborers are paid in some way. The broker and bookkeeper hate being burdened by running the shops, so they eventually all pass into private ownership, so long as any of your workers has enough money to buy one. The shopkeeper isn't very burdened though... they really don't do much of anything. I think anybody is paid a small amount for moving a good to the shop. The shopkeeper just decides which goods to purchase for the shop, and how much to sell them for. All buying and selling is done on the honor system -- they just trade some coins over the the shopkeeper, in return for the object in question. Everybody actually has an "account", which is kept independent of the coins (this is a supposed role of the bookkeeper, although his/her death doesn't change anything). People do grumble if they don't have coins to match their account though, so you have to try to keep coin production up. The bookkeeper constantly hassles you to produce coins if you don't have enough, and if you ignore the mandates, the bookkeeper might become angry and throw tantrums, as usual.
This is all implemented, but is subject to some changes, since I might affiliate workers to workshops more closely, and mess with some other things.