I've had tons of trouble with this. Most of the guides and stickied FAQs are complicating stuff too much.
To record, you need to get your bass's signal into your PC - simply speaking.
Bass -> laptop is possible with a 1/4" to 1/8" cable.
If you want more felxibility, get a USB sound interface ($100-$300). The cheap ones are pretty much equally-bad. I have a Lexicon Alpha. Good enough for home recording.
Regarding hardware, I record with a 5 years old Celeron laptop. Yeah.