Get a basic understanding of modern dance. Because of its diverse nature, you can't learn modern dance from a video alone. A class in modern dance or even in improvised movement can give you insight into how modern dancers use their bodies. Check with a local college or university for classes.
Obtain modern dance videos. There are some instructional videos available for dancers with some modern dance experience, but there are many more that just feature modern dancers performing. You can learn from both types.
Follow along with instructional videos. These videos most often teach you ways to stretch your body and move to tap into a modern dance aesthetic. Modern dance instructional videos may also teach you how to execute specific modern dance moves and choreograph a routine.
Watch modern dance performances on video carefully, both at regular speed and in slow motion. Look for the basic moves that you recognize from your own dance experience. Also look for unfamiliar moves that you believe you can do. You can take notes or sketch some of the moves to remember them.
Clear out your dancing/viewing area so you have plenty of space to move, and dance along to a modern routine on video. You might need to view the routine a few times before you can dance to it. If there's something you can't physically do in the routine, substitute a move that you can do.
Create your own routine once you can dance to the video. Use the moves from the video as the basis of your routine, but choose a new piece of music and arrange the moves in ways that you feel best express the music.