There is one Sponsorship Bonus for each normal Event. When you drive to the event and press
to race, the Sponsorship will be the bottom-right selection.
All you need to do is drive a specific manufacturer's vehicle (BMW, Ford, McLaren, Mercedez-Benz, Hummer, Bugatti, etc.) in the race and get a podium finish (placing 1st, 2nd or 3rd).
It's very simple to buy the vehicles you need because when you select the Sponsorship and the requirement is a vehicle manufacturer that you don't own, it will give you the option to go to the Autoshow and purchase a vehicle from that specific manufacturer. Buying the cheapest vehicle from that manufacturer is recommended since some of the cars can be very expensive.
There are a total of 48 Events in the Xbox 360 version and they are represented by Pink (when new) or Blue (when beaten once or more) circles on the map. If you have already beaten the Sponsorship it will say Mastered when you enter the race menu.