Kreasound has some remix competitions in various styles
Metapop site has several remix competitions running
Splice has some remix competitions
This video describes how to detect the tempo of a track. This will be very useful for making the bars and beats line up with the audio files that we will use for our remix. The first 6 mins of this video describe how to do it very well. It might take you a few attempts to get used to the process. Remember this link is here and you can rewatch the video whenever you start a new remix.
Cardijn Tips for Remix 1