You need a OBD II fault code checking device. They range in price from under $50 to well into the hundreds of $.

Checking the codes is easy. Understanding what they mean can be difficult because manufactures (e.g. BMW) can assign some of the codes as they wish. The information on these manufacture specific codes can take awhile to become 'public knowledge'. Basically you need a code look up table with information about about what a specific DTC code means for your specific vehicle. The more expensive code readers have this info built in. But even the expensive ones usually have a delay for the code info for newer models like the 35d.

Funf Dreisig

p.s. More info on OBD II code readers check out this thread