the larger bottom bracket for one piece cranks is called a "cup and cone" system, with pressed in cups that hold the bearings. you can beat them out with a hammer and a wooden dowel. you don't want to use a punch or a screwdriver because you don't want to damage the cups, 'cause that will mess up your bearings. to install cups, put a piece of wood like a 2x4 over the cup and whack it with a hammer a few times till it seats.
they can be converted to a sealed bearing system like the link BA posted above, and then you can put 3 piece cranks on.
the smaller bottom brackets have a sealed bearing set up, and can only be used with 3 piece cranks. these normally need a crank-puller to remove the cranks, and sometimes special tools are needed to remove the bottom bracket assembly itself.
if you do a search for "bottom bracket removal" you'll find a few sites that will walk you through it, depending on which type you have.