What's sponsorship mean?
Basically, it means a skateboarder gets paid to represent a company. The skater basically becomes a walking billboard for that company. He wears the shirt, hat, shoes, and whatever else that company makes. He skates the deck, wheel, or truck that company makes. It's just a way for the company to advertise, really. It's every park rat's dream come true. All pretty simple, right? Well, not really.

Reality.
The reality of of sponsorship is pretty harsh. First, it's incredibly competitive. Currently there's somewhere around 100 professional skaters, and about 200 amateur skaters. Now, there's an important distinction between these levels of sponsorship, so we'll go ahead and outline the different types of sponsorship:

1. Shop Team: A shop team is a group of skaters (or a single skater) who is sponsored by a skate shop, instead of a company. A lot of skaters start down here and try to work their way up. There's no paycheck involved, but it does mean free stuff occasionally.
2. Flow Team: This isn't much different from a shop sponsorship, but instead you're sponsored by an actual company. The "flow" sponsorship is very informal, and just basically means the company is keeping its eye on you. The perks are shipments of free products from the company.
3. Amateur: ("Am") This is where "real" sponsorship begins. You'll get paychecks and free gear, but it means you have to start putting out for the company. That means going on tour, entering competitions, and filming.
4. Pro: Well, you've made it. Now you compete at the pro level and little kids will ask for your autograph. Enjoy it while you're here.

The interesting bit here is, is that it's up to the company whether or not you're an "am" or "pro". But, thankfully, companies don't just promote people helter-skelter. After all, they represent the company.

The "how to" bit.
First, make sure you're good enough. Companies are swamped with people trying to get sponsored who just aren't up to snuff. There's a few ways to expose yourself to companies, so here you go:

1. The "Sponsor Me" Video: You're filming everything right? Good. If not, you better start. The "sponsor me" video is the most popular way of contacting companies. Put only your best tricks on it, and keep it short and sweet. Edit it down and add some music. Now, send it to freakin' everyone. (Don't forget to include your contact information.) Keep skating and filming, then do the whole thing over again.
2. Competitions: Start entering competitions. While competition ranking isn't a good representation of abilities, it gets you coverage. Also, most major tournaments are covered by skate magazines, so you might get some extra publicity.
3. Travel: Many pros and ams were "discovered" by people they met while traveling around the country. Go skate big parks everywhere and make some friends. Hell, you should probably do this even if you don't want to get sponsored. Either way, it's a good method to get industry contacts.

Well, there you have it. Now start filming every trick and keep dreaming about all the free stuff you know you deserve.