BitTorrent is not a physical program in the sense that you tell it what to do. When you click on a torrent link your browser will either spew forth a page full of garbage, or automatically open the BitTorrent client for you and ask you where you want to save your files, like this:

If you got the page full of garbage (trust me, you'll know) then go back and right click on the file and "save as" the file, then double click it from wherever you saved it at.

Once you select the folder to save to it will start downloading. If you have an older version of the bittorrent client, it will start allocating disk space for the files immediately and not start until that's done. The latest "shadow" version doesn't do this, and allocates as necessary while downloading.

The nature of BitTorrent is pooling bandwidth, so most times you are sharing pieces of the file as you are downloading those you don't have yet. The window will look something like this:

Once you are finished downloading a show you should share it back for awhile so others can finish their downloads. To do this DO NOT click the finish button. Just leave the window open and you will be contributing your bandwidth to the pool. Even a small amount of bandwidth being shared helps everyone out in the long run. It's considered proper etiquitte to share back at the very least as much as you downloaded. If you download a 600mb show, it's proper to keep your torrent window open until your Uploaded: is at least 600mb, or in other words, your "share rating" is green with a smiley face. It's also nice if you can help it, to keep shows open for longer than this, because it does take a while sometimes for people to find out about torrents and they jump on 3 days later, and there are barely any seeds still helping out, so it's difficult to get shows.

Problems:

If you're getting really slow speeds, there could be two problems

For starters, make sure your settings are right. If you're on DSL/Cable, it's a smart idea to set it to "dsl/cable slow", and adjust your upload rate to be slightly under your maximum. For most people, this is 10-13k/s. If you have a more robust upstream, adjust accordingly. If you're on dialup, select dialup/ISDN, etc. Unlimited will generally saturate your upstream and make it nearly unable to do many things, including web browsing, while downloading. Also, this is obviously good if you have a certain amount of bandwidth you can upload in a month and don't want to break your quota.

Secondly, you may be firewalled, or using a shared connection that needs to be routed. If you're seeing a yellow light in the corner, this is probably the case. If you're seeing a red light, that probably means there aren't any seeds for the torrent. You can keep it open and just hope that someone will re-open it, or you can ask for someone to re-share it in the forums. If there's a blue light, that also means there aren't any seeds, but there are other people downloading, so you still may be able to complete the show from them when one of them gets a complete download from a seed they can connect to. If you're firewalled (always yellow, slow speeds usually) check for a solution here or on the forums

And also remember that you're downloading the shows from another person, not a webserver with unlimited bandwidth. Speeds can and will vary greatly, and you may get someone sharing a show that is very slow. Something is better than nothing however, and generally if you leave a torrent going overnight, you can complete it by the next day even when it's going pretty slow. The longer a show has been around, the smaller the chance of it going fast, but it should usually be possible to find someone willing to share a show if you missed out.