Assuming you don't have a pro-level soundcard in your computer you will probably want to buy a USB interface (Check out Tascam interfaces if your looking to keep it cheap). Then, if you have an acoustic-electric you can plug straight into the interface, it won't sound the best but it will be the cheapest and easiest option. The better option is to buy a good condenser mic (for really good recordings two would be the best, but thats really overkill for most people) and plug that into the interface.
Most interfaces you buy will come with software to record with, so you can use that (Tascam comes with Cubase LE I believe) or Audacity, which is free or whatever other audio recording program you wish to use.
Also, google how to record acoustic guitar for tips on mic positioning and stuff. Theres HEAPS of info out there on what are good mics, where to put your mics and stuff like that. It would be a waste of my time to go into any of it as it is already explained in much mroe depth than I could explain it.
^ I agree with everything he's said. For a cheap, but good (i know i'm not the only one around here who uses them) condenser mics, check out the MXL 990/993 combo.


They also do a 990/991 combo that's cheaper and almost as good.

As for the placement of mics, you really have to play with it to get what you're looking for. If I'm using those two mics, I put the 993 about 6 inches away from the 12th fret, and the 990 about 6 inches away from the bridge. You'll have to play with it to get the sound you are looking for though.

Partscaster/Tele into a bunch of pedals, a Maz 18 head, and a Z Best cab.
^^ Yes, there is no one perfect way to get a good tone everytime. You have to experiment with the song you're playing, whether you're strumming hard, fingerpicking, etc - the room size, shape and contents, all that comes into play and will affect where and how you mic it.

Try a lot of different things, you'll figure out which your particular session needs - bassier, more treble, less volume, more volume, thinner or thicker pick, etc.
- Fender, Taylor, Martin, Ibanez, Ramirez, Marshall, Boss, Morley, Mesa/Boogie, Univox, Shure, Monster, Dunlop, Seymour Duncan, DiMarzio, Lace, Sperzel, DW, Tama, Zildjian, and a little Johnnie Walker