well... what you could do right off the bat to get started, is drop a little cash on the following- assuming your cimputer has- a sound card- with probably an 1/8" stereo "line in" input- not mic in (think little headphone type) if your computer is equiped with the sound blaster variety of card-
-get a recording software- download demos- pick one ya like- N-tracks is pretty cheap- ask around and do a search to find some popular software apps- ($50- $500)
-get a cheap rca to 1/8" trs cable to plug into the line in on sound card on the dell- this will connect your drum machine to your puter ($5)
get a decent mic and preamp and make similar connection to the dell- the software that you get will be able to multi track- that is play a track while recording another- so that you may be able to combine them into one stereo track for a final (mic and pre- $150- $5,000 and up)
youll need something to listen back on- headphones for tracking(think singing vocals over the beats) and monitor for mixing- speakers with an accurate reproduction of sound- search around here for monitors ($200 and up)
the above will get you started, but is not ideal- eventually you'll wanna be gettin a better soundcard (maybe sooner than later if yours makes alot of noise or sounds bad)
im sure others will add- jeff