Why dovetails? Those matter in furniture that is going to be subjected to some stress, like drawers in a chest. You are (presumably) not going to be slamming the tapbox. Know anyone with a biscuit joiner? That should give more than enough strength for your purpose. Though I have one, for my keezer collar all I did was 45* miters on the table saw, Titebond glue, clamped them, then glued blocks inside the corners for added glue surface for strength. The blocks add some peace of mind, but are probably overkill. I made it only using selected cedar 2x4s from Lowes. If it were not for the flowing beer I would be embarrassed by the woodworking. I did bevel the corners for show. It does the job I still steadily get compliments on the collar. .
Much of the time dovetails are done as an aesthetic choice or a display of skill. If you just want to have a working keezer, glue and some evenly spaced screws, or even just brads, will get you going. In your circumstances I'd buy a box of colored star drive screws (meant for decking) which will probably come with a Torx bit in the box. If you place them symmetrically it will look good enough, and the beer can flow! However, if you really want dovetails, here your go:
http://www.woodcraft.com/Articles/Articles.aspx?ArticleId=249
They show fine tools, which of course they sell. You could do it with a passable back saw and sliding T bevel, which won't cost that much. By the time you finish the 19 in box you'll have enough practice to be pretty good at it! Or maybe by that point you'll be buying a replacement) plain board and some star drive screws.....
I'd love to see pictures when you are done.