I have done this with FRAPs as a cheaper method vs Camtasia.
I like that FRAPS is lossless and I already owned a licensed copy of it. With FRAPS I would get the music ready that i want to add to the video. Have FRAPS ready to record. Shut off the audio on the Media player so the sound of whats happening in the video doesnt mix with the music. And quickly do the following.
Start Music
Go Full screen for video
Press the FRAPS hot key to start recording the video with the audio that is playing.
When video recording is done press hot key to stop it from recording.
Then I use VirtualDub to take the newly created video and make it into a smaller AVI file for youtube or sharing with friends. FRAPS makes like a 2GB file of raw video and audio information LOSSLESS and VirtualDub encodes it to smaller AVI or other format of choice. Depending on the settings you go with it will keep video sharp or make it lesser sharpness. I go with H.264 codec for best quality to size file in the end.
VirtualDub is free, but FRAPS comes at a cost.