Yes, you can use your own guitar to record, however, the biggest problem most people have is due to their sound card not being up to the job. also make sure your computer is up to the job.
you might be able to get your onboard sound card to work with MC, but you might not. even if you get it to work, it's not going to give you the best quality. If you have a PC (not a laptop), I recommend a good PCI sound card from my list. If you plan on doing any vocals or mic'ing of your guitar, you'll need a decent mic and a mixer (or some type of preamp). The behringher Xenyx 802 is a great little mixer to start with and it's only $60, I think.
Here's my sound card advice:
http://homerecording.beaglesound.com/9.html depending on what type of stuff you're going to mic, a great starter mic is the Shure SM57 or SM58 (same mic, really, just a different windscreen). you can get one of those for about $100. a condensor mic will give you some warmth added to the recording, a really good combo purchase that will give you a vocal mic and an instrument mic for $100 is the MXL 990/991. search for that on musicians friend or guitar center online.
If you have a laptop, the mixer and mic are still recommended, but look at that webpage for info on Firewire or USB instead of PCI.