Find out what your street skating strengths are. Are you good at grinds? Flip tricks? Whatever it is, find locations where you can do tricks that emphasize your strengths.
Find a friend to film you doing your tricks and make sure he gets lots of footage of you doing all of your best tricks in various locations. Make sure you have some diversity in the tricks to show your versatility as a skater and your abilities in different aspects of skating. For example, don't send in a video that only shows you board-sliding different rails. Throw in some other tricks to keep it fresh and interesting.
Go through the footage and edit out what is bad. Pull all of your best moments into one video. Generally, videos for sponsorship should be concise--about three to five minutes long. Leave the sponsors wanting to see more. Find a cool song to add to your video to add to the emotion and make it look more professional.
Contact the Nike Skate team and tell them you are an amateur skater looking to make the team. Tell them you have a video of yourself and ask where you can send it.
After you send in your video, follow up if you do not hear within a week. Be persistent. If they do not accept your first video, work on new tricks and put together a second video to send.