Well here's what you need:
Computer
Recording Software
Converters (Analog - Digital/ Digital - Analog)
Microphone/s
Microphone Preamplifier
Speakers
Cables
There's a million different things out there and a million things to consider. A decent cost efficient tool is the Line 6 UX8. This will give you:
8 A-D Converters and 10 (I think) D-A converters + 2 (maybe more) Digital outs.
8 Microphone Preamplifiers
I believe it comes with recording software too. Definitely comes with guitar software and quite a bit of effects and processors
Just leaves you with some mics and some speakers, assuming you have a computer. There's so much more you'll want to get though to make your life easy. The right headphones, possibly a controller for the software. You might want different software than the stuff provided by the line 6 unit. But in any case, if you want to get started this a good place to start IMO. If you think 8 mic pres is excessive than you could check out the UX2.