this is how I do it

others feel free to jump in at any time)
there is only money involved if you want there to be but in general: there is no fee to set up, if you are going to be the contact person for the store, you coordinate with them on dates. find out what other swaps are going on close by so you don't have a conflicting day. make sure the "store" carries the event insurance, some make the person running the swap have it and personally, I wouldn't want to foot that bill if you are not taking in any money to set up. the store is actually hosting the swap and you are informing people it's going on and when (the store will as well)
I advertise in any free publications, you can let the newspaper know, you could have a demo of some sort (neutering and butchering are frowned upon by some audiences so make it public with children friendly)
let people know the swap rules, there is a long list on the beginning page, those are state rules. I also incourage people to clean up after themselves so we will be invited back. make it look good for the public or they will shut you down.
most of the stores I have talked with really like these swaps, they are a win win for everyone. the sellers get to market their items (birds, crafts, products etc) and the store gets to sell add on items (those chicks will need food, waterers, feeders etc) and the public gets to get info from sellers on care of their new purchases, face to face. If I have a problem with something someone is doing at the swap, I will quietly take them aside and let them know, what they do with that is up to them. there are on occasion, inspectors that come around so if someone is not following the rules, THEY are the one that is going to have a problem, you warned them.
pm me if you have any other questions.
I am working with the waterville
TSC to see if swaps would be possible there as well.
What would it take to run one? Is there any money involved? Or do I just have to organize it? I am a teenager so I'm not entirely sure that I would even be taken seriously by TSC... They would probably want a "responsible" adult running it (I am very responsible, but teenagers in general have ruined it for those of us that want to do serious stuff.)