Here are some general guidelines to getting fast connections with BitTorrent.

• Give it time! Be patient! This is the most important suggestion for most speed-related problems. Sometimes it can take a while to contact a slow tracker. The beginning of a download will be especially slow since you don't have any pieces of the file to share with others. Recently, trackers have been quite overloaded and it's common to get timeout-related errors: see I'm getting an error message, what does it mean?. Leave the client open and eventually it will connect.
• Make sure the torrent is "live." Use an experimental build of the client that shows the number of peers and seeds to which you are connected. Or, check the status of the torrent (using the website's statistics or TorrentSpy) and make sure there are other people connected. To get decent speed, a torrent must have at least a few other people connected. The more peers, the faster the transfer will be in general.
• Sometimes, limiting your upload rate will increase your download rate. This is especially true for asymmetric connections such as cable and ADSL, where the outbound bandwidth is much smaller than the inbound bandwidth. If you are seeing very high upload rates and low download rates, this is probably the case. The reason this happens is due to the nature of TCP/IP -- every packet received must be acknowledged with a small outbound packet. If the outbound link is saturated with BitTorrent data, the latency of these TCP/IP ACKs will rise, causing poor efficiency.
  
  Use a client that allows limiting of the upload rate, and set it to around 80% of the maximum rate observed. It can be tempting to limit the rate to very small values. On very healthy torrents, this will not adversely affect the download rate. However, when there are fewer peers you will generally get higher download rates by allowing the highest upload rate possible before saturating the link -- the (approx.) 80% sweet spot.
  
  To limit the upload rate with Mac OS X, try Carrafix. You'll want to set an individual cap for each BitTorrent port (6881 and up.)
• Ensure that your network allows the outgoing connections necessary for BitTorrent to work. Some networks (usually at schools, workplaces, etc.) are firewalled and all connections must go through a proxy server. In other cases, only well-known ports are available. There are too many different situations to list every possible scenario, but if you are trying to download a torrent that you know to be "live" yet the client still reports zero peers and seeds, then this is probably the case. See also the question Can I use BitTorrent with a proxy server?
• If your network uses NAT, make sure the BitTorrent ports are forwarded to the machine that runs the client. This will allow inbound connections from peers. Otherwise, only outbound connections will succeed. See the section What ports does BitTorrent use? Will it work with a firewall/NAT?
• If you have a software firewall, make sure the BitTorrent client has the proper access.