You can use any remote control have lying around handy with lirc, you just
have to let lirc "learn" the codes and then assign them to tasks. This is
the easy way to do it.
Now if you still want to build your own transmitter then you need to study
up on the various protocols to get a feel for how they work. Then you pick
one (or design your own) and go from there. I would use a PIC, but you
could do it with more parts and not use one. Usually you have a carrier of
about 38kHz that is modulated in some fashion, usually by switching it on
and off. RECS80 and RC5 (not to be confused with RC5 encryption techniques)
are two popular protocols. This should give you a decent list of things to
Google so have at it a bit and come back with more questions.