Most people think mixing is complicated. It's really not. You do not need specialized software. All what you need is a voice recorder software, audio player, sound card and microphone.
For example, you wish to mix together your voice from microphone and backing track. You can do this in real time. This guide will help you do this without extra cost.
Run the downloaded file and follow the installation wizard instructions.
I guess that the microphone is already connected to your sound card. In any case, make sure it is enabled.
Second, run the audio player and load backing track. Adjust the playback level.
Check the microphone and adjust signal level by VU-meter. Windows lets you configure microphone gain via Control Panel.
Are you ready to make the first test recording? Fine! Start playback in audio player, click the Record button in voice recorder and perform the song.
After recording finished you can playback it and if you not satisfied then go to the step 4 and change your setup.