It should be quite possible to hear yourself while singing. Are you able to record yourself for playback later? If not, down in the lower right-hand corner of your monitor next to the clock you should see a little icon that looks like a speaker. If you don't, click the < arrow to show more icons, and it should be in there. Right-click the speaker, then click on "Recording Devices." Inside there, select the Microphone port and click "Set as Default."
Then you should be able to open up an application that uses the microphone and start singing. It may be hard to hear yourself over your own singing though, so you may want to try it through a decent set of headphones.
If you can get over the minor insult in the title, the "______ for Dummies" series is really good for beginners. (PCs for Dummies, Windows for Dummies, etc.)
