How often to replace a chain: lots of possible answers to this question. A chain absolutely has to be replaced if the chain skips over a cog tooth while riding and hammering hard. If you let it go that long you probably have to replace the cassette also, but that's OK if you don't mind the expense. You can also buy a little tool called a chainchecker that will tell you when the chain has stretched 0.5% or 0.75%. Velogirl recommended 1500-2000 miles for chain replacements to avoid having to replace the cassette too (though eventually the cassette will wear out no matter what).

I wrote a very detailed description of how to break and install a chain with a chaintool in this thread: http://forums.teamestrogen.com/showthread.php?t=9930

Powerlinks/masterlinks are the way to go when installing a chain so you can break it again easily without a tool for cleaning. But you'll still need a chaintool to cut the new chain to length (based on the old chain length if using the same sized cassette).

Type of chain: they are sold as 8-speed, 9-speed, or 10-speed chains, based on width. Must match you cassette. Also probably best to stick with Shimano if your drivetrain is Shimano or Campy if your drivetrain is Campy. I use 8-speed SRAM chains on my 6-speed freewheel (you can use a narrower chain than necessary, but not the other way around). Ask for a recommendation at your LBS.

This thread has info on replacing a cassette and on chain replacement times:
http://forums.teamestrogen.com/showthread.php?t=9185