I've used USPS, UPS, and FedEx to trade. I like UPS for small trades and I use the flat rate boxes. FedEx by far is the best. Print the shipping label at home and drop it off without having to answer any questions.
Is it against the law to ship beer? Yes through USPS. They won't prosecute, they just might snag your stash. FedEx and UPS it's against their regulations...they have returned it in the past. Some businesses get a permit to ship, that is how beer/wine of the month clubs get around it.
The real secret is packing it! Use baggies, tape lids etc...google will show you how to ship beer.
Trading can be expensive, but so is any other hobby. If it wasn't for TG, no one would really want to trade with people in Iowa. I've found that TG can stand up to any beer in the country at this point.