If you connect a mic to your computer, you should use the mic input (sometimes a pink connector), not the line input.
Second, computer microsphones are the electret condensor types. They need power, which is supplied by the connector. If you look at the plug of a computer microphone, you see three separate metal parts (tip, ring, power). If you bought a dynamic microphone (they can sound much better) you may have trouble connecting to the soundcard in the computer.
Finally, use the audio tuning wizard which is present on XP and later. Go to Control Panel - Sound and Audio Devices - click on the Voice tab, and click on "Test Hardware." AFter testing the hardware, a window shows the microphone test, which can be used to calibrate the recording colume of the microphone. Speak fairly closely into the microphone, but keep your mouth one inch from the mic element. Usually this gives good results.
Webcams have often microphones built in. They are good for conversation but not much more. For things like Skype or language training, you can buy a headset with attached microphone. When you calibrate those, they give excellent and clear results.
For real audio (vocals, instruments) recording, you should probably stay away from the computer and work with a digital (hard disk or flash) recording device. The computer is simply too noisy for good audio recording, especailly natural (unamplified) instruments. But once you have the audio recorded in digital, editing the audio on the computer works very well, especially with good software like sony soundforge.