Getting good moving footage of skateboarding can be difficult, there's really no safe way to do it without putting either yourself, the skater, or the camera at risk of getting broken. Regardless, skaters will do it anyways. One of the most popular methods of doing so is using a follow car, and driving no more than ~10 feet behind the skater. Here's an example of that:
This is my good friend Liam Hayes, skating down a famous run in Malibu, CA. This entire time, the follow car (driven by Alex Ameen), is ridiculously close to him to ensure good footage. Most of the time these videos are shot on a DSLR, with a wide angle lens or a fisheye at about 8-15mm focal length.
Here are some pictures from other angles of shooting follow runs.
In this last picture, you can see two DSLRs, as well as extra lights attached to the car. Two cameras ensure different angles without having to drive the run multiple times, and the lights are attached for various reasons, often to shoot night follow runs, as seen in this video:
I've driven and skated during a few follow runs, and its equally scary to be in each position. When skating a follow run, don't look back! You have to have insane amounts of trust in the driver not to get too close to run you over, and believe me, it gets too close for comfort too often. Being the driver, you have to make the decision of where the safest distance to follow from is without sacrificing the quality of the shot. Normally I try to stay ~7 feet behind the skater, but this can be difficult on open roads with speeds of up to 55+mph. When driving that close, you can barely see below the skaters butt over the dash. Here's a screenshot of me getting a little too close to my friend, Dan Snyder, on a follow run I drove.
Overall it adds an extreme element of danger to an already ridiculously dangerous sport, but its worth it to get the shot!