I was in a simialar position as you about a year ago,and perhaps I can help you get started.
you only need two things to play doom :
a source port: doom legacy,zdaemon,zdoom,prboom,eternity engine,jdoom,vavoom,boom,glboom,skulltag,zdoomgl
all of these are free.
a iwad: doom.wad,doom1.wad,doom2.wad,tnt.wad,plutonia.wad,freedom.wad
if your using windows xp it might not have .wad at the end
ok so what you want to do is download a source port,I would suggest doom legacy if your kind of new to computers and don't know how to use the command line.It also has very good documentation and is very easy to use.jdoom and vavoom are also very easy to use.
then make a folder put doom legacy(or another source port) in there and doom2.wad(or any of the others listed in iwads)
then run legacy or whatever
this includes most of the ports and also a launcher for them all it's worth a look as long as your not on dial-up ;):
each of the source ports have different features, jdoom tends to focus on graphics while zdoom adds a whole slew of new things that previously were not possible.Just remember to give each source port a look before thinking it sucks.Most people who have been around for a while, prefer zdoom because pound for pound it has the most features.