Going the "all computer" route....
You need some sort of interface to get the guitar into the computer. You can get a USB interface that has a guitar input on it. Personally I use an M-Audio Fasttrack PRO.
Then you need software. Cubase, Pro Tools, Logic - take your pick. I've used Cubase and Logic, and now I use Reaper. There's a uncrippled demo version available, and it's about $50 to buy. Think of this as you're multitrack recorder.
You'll need effects for your guitar. Amplitube and Guitar Rig are two commercial packages. There are also a lot of freebies about. They're not as polished and sometimes you have to stick a few together, but you can get good results. These are your effects, and guitar amp.
If you're not recording bass, there are free bass guitar synths. Can't recall the names, but Google is your friend.
Drums. Never been down the free route. Toontrack EZDrummer is a good starting point for not much money.
Vocals. Many of the interfaces will take a mic fine. All the processing effects are again freely available.
After that, it's just many many hours getting familiar and sussing out what works for you.
Don't be fooled into spending a lot of money!
If you go to my music page
http://www.eightdeadlywords.com/music.htm, nearly everything was done inside the software. Most of it was free. We only recorded the drums in a studio, and to be honest they were done in 2 sessions costing us about $40 a session. EZDrummer will do a pretty good job. I've got links on there to most of the software.
Hope that helps!