I've bought the stands given by the Local Leader level 2 perk. I've already assigned people to it, but it doesn't seem to work. How does it work?
Each stand does something a little different obviously by the name of it. When you assign someone to the stand you can talk to them during the day to buy and sell things to the person assigned to the stand. If you talk to them at night you can only trade items they have equipped. It doesn't matter where they are when you talk to them, as long as it is after 8AM, you can still buy and sell things.
The general store stand will also raise the happiness of the whole town slightly.
The stands also start slowly depositing caps into the work bench of the town they are in under the misc tab. They will deposit more caps based on how big and happy the town is.
Right after you assign them to a store, they will usually start walking to it and position themselves behind it. At that point you can start bartering with them. However, their inventory usually empty at this point. For me, sleeping for a couple of hours did the trick.
I noticed that some people are really not in the mood for working with you, Marcy Long in Sanctuary for example. I assigned her to a store and she just kept doing whatever she wanted in Sanctuary, although still offering the store inventory when talked to. I'd advise against using her for a store...