Connecting a guitar (or any electric instrument) to a computer is not as straightforward as you might hope, no matter what software you're running. While your soundcard probably has a stereo jack in and a guitar has a jack socket you probably realise that just plugging one into the other wont get you very far.
If you're desperate and have fairly hot pickups you may get away with plugging into the microphone input and cranking the volume up, but this isn't going to sound great. What we need is amplification.
Most home-targeted amplifiers now come with a headphone/line-out socket (often dual-purpose: there is actually a difference between the two, but they cope with it). Your 100W Mesa Boogie wont (no, I don't have one either), but solid state, modelling amps and mini valve-amps like the BlackStar HT5 typically do. A headphone/line amplifier like a Pod doesn't have anything else. This is what you want to plug into the computer's line-in and, while it wont sound quite like mic-ing the cabinet itself, they will (even on the valve amps) include some degree of cab modelling.
But there's a catch: your computer has all kinds of other things plugged into it. Connecting your amplifier into a sound card creates unintentional circuits, at a minimum round the power lines between your amp and the computer. The classic 'ground loop' occurs when this circuit picks up mains noise (50Hz hum, or 60Hz for North Americans). This is the type of noise humbuckers are made to reject, except the noise isn't coming through the pickups it's being added on the way to the soundcard. There are other sources too: the first time I tried this I heard about two clicks a second, that's not mains hum. It turned out to be my monitor power supply, leaking via the monitor connection into the computer. Disconnecting the monitor everything was fine, everything except that my monitor was unplugged.
What to do about this? The solution is quite simple, break the circuit that flows around from the amp to the computer over the soundcard connection and back via the mains. If you're using a laptop you could just unplug it and run on battery. But on a desktop system there's only one place you can do that safely and it's on the line-level (sound) connection, where the voltages are not going to leave you extra crispy if something goes wrong. This can be done with a very cheap device called a "ground loop isolator" - google it or look on your favourite shopping site, they are typically used in cars and cost about five pounds.
This often barrel-shaped device is essentially a pair of transformers which decouple the direct electrical connection but still allow sound through (or if you like, imagine a tiny speaker and microphone in there). Unfortunately they most often have RCA plugs, so you will need a stereo jack to RCA converter for both ends: one will probably need to be RCA male and the other RCA female, but check the connectors on the isolator. Of course you were going to need a cable to connect things anyway. There are other ways to do this, but this is the simplest and cheapest.
A quick mention on soundcards. On-board computer sound (built into the motherboard) is noisy. If you don't know what you've got odds are it's onboard, if you're on a laptop it's almost definitely onboard. You can hear the machine doing things in the background, this is not ideal for recording unless you're really into abstract electronica. There are two ways out: get a usb soundcard (this is your only option if on a laptop) or an internal card (PCI) which will require opening the computer and best check before buying one that you actually have a spare slot for it.
Both USB and internal sound cards can range from the very cheap to professional recording with multiple channels (unfortunately the latter aren't necessarily good for playing games on). Actually there's also firewire at the professional end of things, but if you're considering that then I doubt you're reading this blog.
Speaking of USB and FireWire, you could avoid all the above messing about by using an amp or processor that can send sound over those. To the computer it looks like an audio interface and since the signal out is already digital you don't have to worry about noise being added after it's left the amp. This used to be limited to higher-end effects processors, but modelling amps are starting to show up with it now too, for instance Fender's Mustang amps and Yamaha's just-out (and rather expensive...) THR. SPDIF is another digital standard, but you'll likely only find it on professional rack units (and probably wont have anything to plug it into at the other end).