okay... so yeah, you buy a domain.
www.godaddy.com seems to be the company du jour for getting .coms, although my personal fave is
www.obantec.net, because the chappie there is very nice and has done Good Things for me.
anyway, yeah, you buy the domain. quite often the people you're going to host with will sort that out for you and if you don't knwo much about it then that's probably a good thing although it may cost a bit more than going to a company that just does registrations.
a hosting company will sell you a chunk of disk space and give you some details about how to upload files onto thier server... if you've bought the domain name off them too then they'll sort out pointing it to the right place.
you put the files up, and they serve them out.
redirection is quite simple - the same sort of idea. say i've got some ISP webspace that anyone can look at - say www.myisp.com/users/d/da/dan/index.html, well you can see that's pretty pants for a business. the cheapo thing to do is get a "redirect" from a domain selling place. they'll make it so any browsers looking for www.dan.com actually go look at the myisp.com site instead.
that's the executive summary anyway... more details available on request