Depends on the type of sponsorship you want...
-Most large named companies have their own employees drive the "sponsor car". Other are looking for everyday people. All you need to do is apply. Send a resume and profile about your present and past cars. Tell them about your plans, your accomplishments, and why they should choose you. Call their headquarters, and find out if you can meet in person with a regional manager in your area. If they like you, most likely, they will give you parts at a great discount or for free, but you are usually required to attend specific shows, and a certain number of shows per year. And if you do bad, because of you, they will drop you and ask for their parts back. Some companies will let you keep them.
-Become a guniea pig. If you notice there aren't many companies making parts for the 2.5L duratec yet. And it's been around for about 6 yrs now. Contact companies that make products for cars. And offer to let them use your car as a tester car. I've known people to get completely free turbo or SC kits. You save them $20,000 from bying a new car, so the least they can do is give you a free $3000 kit that only really costs $1500. I personally got great discounts on my previous car for letting a company do work on my Probe. It was well worth it, but I have to warn you. Your car may have problems as time goes on since you are like the prototype, and all prototypes have bugs.
-Instead of going to a manufacturer, go to a licensed reseller of many companies parts. Many of them want their names spread around, so if you put their custom graphics on your car and attend one show, or race, or whatever, they'll cut you a deal on parts they sell. Usually all you need to do is contact the owner of the store, and ask them if they are interested. Finding someone who has sponsors who can introduce you to the right people and maybe give you a recommendation, can only help.
It's not easy, and most likely 99% oif us have no chance, but it doesn't hurt to ask. Start at yout local perf. shops, and work yourself over the internet.