So here's my situation. I've got a good laptop, and use Audacity. I want to record vocals, acoustic guitar and piano.
Somehow the mics I have aren't compatible with the computer, so all I have is the dinky little built-in one.
I could REALLY use some help here. Thanks.
Well, uh...Alright, this is gonna be a lot of info, some of which you will have to look in further yourself.

Anyways, first off, download Reaper. It is vastly superior to Audacity, being a true DAW, and it is still free. It will seem a bit much at first, but you'd switch to it in the long run anyways, so it's better to start early.

Secondly, what mics do you have? If they can't plug into your computer, you probably should look into a USB interface. You will NEVER get a good sound with the built in mic. At all, so just forget that idea. The interface will allow you to connect the mic to the interface, which will run into a USB port on your computer and record into Reaper. One with phantom power and a few inputs will run about $100-$120 used, such as the Lexicon Lambda or M-Audio Fast Track.

Third, if your laptop is good, it should be plenty fine for recording, so don't worry about that unless you plan on using a ton of effects or doing really heavy electronic music.

Fourth, recording a piano is tricky business. Three condenser mics would be best, two would sound good, one would be acceptable. It would be tough to do it with a single dynamic mic, which is likely what you have since you're new. You would be able to record the guitar and vocals with a mic such as that, though it might not be as good a quality as you'd want.

This should be enough to get you started. If you want suggestions on possible gear/interfaces/mics, then posting your budget would be helpful. But keep in mind, using Audacity and a laptop mic, you will NEVER get a sound that you'll be happy with.
Check my post above. What he's saying is that your computer needs a way to convert the analog signal from your instrument/mic to a digital one that can be recorded to your computer. An interface does this in an efficient way. It will vastly improve your sound quality.

Edit: Feel free to PM me with any questions you might have. I know this can be confusing, and you'll likely get a lot of different answers here. You'll soon learn who to listen to.
Last edited by CrossBack7 at Jun 13, 2011,
Errr, I would highly suggest getting new mics. At least get an AT2020 USB mic. It would let you record guitar and vocals to a good quality, though it wouldn't be very great for piano unless you wanted it as a sort of distant sounding background-ish effect. I think it runs about $100, and you wouldn't need an interface for it. You'd still want to upgrade eventually though, as it's very tough to record a piano well without at least 2 decent mics.