If you see a broken icon, you need Quicktime Player. This free application is easily installed following the instructions on the Apple website.

If the movie has not started to play, it is still downloading. Quicktime analyzes your connection speed and decides when to start playing while downloading the rest of the movie in the background. The slower the connection speed, the longer it waits to start playing.

If you can see that the movie has partly downloaded but hasn't started to play automatically, click the little forward arrow at the bottom left. If the movie skips or pauses at any point, you can drag the playhead (the moving circle at the bottom of the window) to the left in order to replay any portion of the movie.