Well, you've got two problems... one, you're using a Microsoft program to get something meaningful done (ohhhh, snap!) and two you really should be using a better microphone than a computer mic, they tend to be pretty low in quality and high in noise.
So what you need is a multitracking program, one that can record a track, then record a separate track, but still have both of them loaded so you can jump between them, or add another, or whatever. There are a wide number of programs that can do this, from free programs to the most expensive piece of audio software I've ever used (Samplicity, 1400$, and man is it cool!).
I second the suggestion to try out Audacity. It's free, it's pretty simple to use, and you get some effects to go along with it. If you want to go to the next step, I'd suggest Reaper (link below). It's a little more complicated to get into, but it makes more sense to me and has fewer extra (sometimes useless) bells and whistles and visual distractions than other programs. Oh yeah, the unregistered copy is free, which helps! (uber cheap to register, too, which is nice)
As far as sound goes, you can stick with the computer mic and mic in jack, but as you'll notice your recordings will be pretty low in quality, lots of static, lots of fuzz, and pretty limited in meaningful frequency response (ie no lows, poor midrange, etc). I saw a mic at Wal-mart the other day for just 10$ that I'm betting would be better than what you're using now. You want a unidirectional dynamic mic, it's the easiest thing for you at this point. Point it at something, and it records it, no external power or worries about it picking up things behind it, etc.
Now, ideally you will someday get a better microphone. The Shure SM57 and SM58 are great mic's, probably the best mic's you can get for the price. They're built well, very durable, and sound great. They're usually around 100$, and I actually saw some on sale a month or two ago (first time I've ever seen them on sale!) for a little less. The '57 is best for instruments, as it has a flatter frequency response, and the '58 is better for vocals (and possibly violins and other stringed instruments). Both can be used for either with decent results, though. The SM57 is *the* classic mic for mic'ing an electric guitar, though, so you know.
Of course you need to get the sound into your computer. You can use the 'mic in' and 'line in' jacks, but the ones that come with your computer tend to be pretty noisy, and that can affect your sound quality. There are a few ways to go, but probably the easiest is to go with a USB audio interface. I think the results are just as good if not better than a good sound card, and of course the USB interface can be used with multiple sound cards. I'm using a Lexington Alpha, it's a pretty basic unit but I got it for less than 200$ (no idea what exactly, you'd have to look it up). No noise, at least nothing you can hear, and you can plug mics, guitars, mp3 players (with an adapter) etc in to it all equally well.
I'm using a Toshiba laptop with the Lexington Alpha and a decent set of headphones as a part of my mobile recording setup, actually. It works out pretty well, I can bring it to work and jam out during lunch. =) Nothing like jamming to a drum track or working on a song during the day, it really relieves a lot of stress...
This is very important. ASIO drivers. Try downloading ASIO4all, it's a free program that supplies low-level, low-latency drivers for your sound. You need to find a program that can use them, but it's a hell of a lot better than using the drivers that come with Windows.
Ever play or sing a note then hear it on your laptop a half-second or second later? That's called latency, and it is evil. ASIO has the least latency you can get. If you want to record several instruments, or play or sing to a backing track, you need the lowest latency possible, and that doesn't just mean not running other programs while recording, it means getting the best drivers you can. The Lex Alpha comes with its own ASIO drivers, or maybe I had to download them from Lexington, I don't remember. Either way, get them.
When you start getting a grip on all of this, start thinking about getting a condenser mic. They require phantom power, and it might be worth it to get a USB interface that has phantom power in it for when you do go condenser, but the quality of sound is sooo totally worth it. Condenser mics tend to have excellent top end quality, ie, they capture a lot of the high-frequency information (transients, etc) that your normal dynamic mics just can't. Really the best way to go for vocals and string instruments especially. They're studio mics, you can't use them live (too hot) but if that's not an issue... I don't suggest them for the beginner (no offense) just because they're not as sturdy as the dynamic mics... you've got to be careful with them, and it's a good idea to get used to recording with a mic that won't ge