Bit Torrent is a simple way to download basically anything at high-speeds by taking advantage of multiple sources. It is known as peer-to-peer downloading because you are downloading from other folks, rather than from a central server. Further, you are uploading at the same time that you are downloading, thus making everybody else go faster too. The more folks downloading, the faster it goes!
Anyway, the first thing you will need is a bit torrent client. There are quite a few to choose from. Personally, I use micro-torrent, which is available here. It is simple and doesn't take up a lot of space. After you have a bit-torrent client, you need to find some shows. For most jam band shows, the place to go is etree. If all you want is Phish then click here. If you are looking for the best source from this tour, click here. What you see is a list of currently available shows. Notice on the right the number of seeds. The higher the number of seeds, the faster the download, generally speaking. Just click on the name of the show, and then click on the torrent file (which is to the right of the category "torrent"). It also says "click to download." Just pay attention to where the file downloads too (but you should know that already), in general, micro torrent will put the file in the download folder under my documents (for PC users).
Now you've got a fresh flac or shorten file, what the heck do you do with it? Some folks use programs that play flacs and shn's directly, but I use iTunes to serve to my home stereo and for playback on my iPod. I will walk you through creating files that will work in iTunes or to burn to CD. You will need to download a program called Traders Little Helper. It lets you convert basically any music format into any other music format. Open Traders Little Helper, click on open "Format", then click on "Decode Audio Files", click on "Add" and then select the files you downloaded. This will decode your downloaded files to wave files, which are suitable for burning to CD. Just open your CD burner and add the files and you are done. If you want to use iTunes, drag the wav files into iTunes, rename them and then convert them to Apple Lossless Compression. Do not use AAC unless space is a major premium.