When it comes to purchasing a vehicle with either a low score or little to no credit history, it makes it difficult to get approved. It is not impossible, just most banks / credit unions will have standards that need to be met before they loan you the money. The biggest thing that can help you buy a car is putting a large sum down. Trades with positive equity help, but the banks still like to see cold hard cash.
Also, if the banks have standards that need to be met, they normally mean that they will not finance anything that is over 3 to 4 years old and cannot be more than 11k dollars. Which limits you to the choices of vehicles you can get.
Best case scenario for you is to have some money down with your trade. Most dealerships now will work hard to help make you a deal and get you approved.
Good luck and happy hunting!