Audio/video syncing

Hello,

I'm trying to create a course in which I want to include a movie, where I describe how to do something in a different computer program. I recorded the movie and separately I recorded audio (thx guys for discussion on microphones! helped me a lot). What I need to do now is to adjust my video (cut out some parts, make some pauses) and add audio to the movie (which I need to cut as well as it cant be combined with movie as total times differ).

Could you recommend me software where I could cut video in pieces - add to each piece seperate audio and then combine it back in one movie once again?

Thank you for your help!