Assume a universe depressingly like ours, in which special relativity holds. No hyperspace, no warp drive, no wormholes, and even the limited get-out clauses offered by real world physics either don't exist at all or are not practical. [Added later in response to comment by Fhnuzoag: no ansibles either. Neither material nor information can travel faster than light.]
I can think of a few ways that trade between star systems might take place. Emphasis on the word "few".
Information can be sent by radio. Trade in knowledge between Earth's system and e.g. Alpha Centauri is practical, assuming that either alien evolution or a previous human colonisation effort has put anyone there to trade with. But it is still so slow that a human lifetime could get used up just straightening out the terms of the contract. Still, human institutions can outlive individuals. Possibly networks could build up where Star A talks with Star B which in turn talks with C and so on.
For anything other than very nearby stars even lightspeed information transfer takes anything from thousands of years to an arbitrarily high limit. So if the nearest star systems are not inhabited the only way information trade can take place is if the inhabitants and/or institutions are very long lived and don't mind receiving payment thirty thousand years later.
Trade in goods, or trade of goods for knowledge, has all the problems above multiplied a thousandfold. Certain authors have plausibly sketched out small payloads of high-tech stuff being sent out by automated Bussard ramjet, e.g. Larry Niven's A Gift From Earth, but that isn't really trade, as the title of the book implies.
Perhaps the most likely model is generation ships (or ships with long-lived nonhumans aboard) plying the spacelanes. The ship has a large population and the capacity to grow food, create technology and art, and to mine or otherwise gather raw materials. The ship as a society can trade with the people of the planets it visits. But that is only going to work if an implausible proportion of stars have inhabited planets. What if they don't? A generation ship that goes 1,000 generations without meeting anyone else is for all practical purposes as isolated as Earth is now.
I had some brief hopes for trade with hive-minds spread out over multiple star systems. It won't work. If the thought of the hive mind takes place at lightspeed or less, trade is constrained by the same problems as above. The thought of the hive mind cannot be instantaneous because (as I may have mentioned) faster than light travel is impossible.
Any better ideas?