When financing a car, there are a few things that you'll need before applying, as well as documents that will be required during the Loan Origination process (This is when your loan is being created by the finance company).
First of all, you'll need to know that there are different ways to finance your new car (whether you're buying a new or used vehicle, for the purpose of this article - it is new to you). For this article, I'll focus on an auto purchase (instead of refinancing an existing loan). You can finance your purchase through a direct product. This means that you apply directly to the finance company. You can also receive financing indirectly. This means that you apply through a third party (usually the car dealer). In this scenario you'll sign a contract with the dealership, and the dealer will sell that contract to the finance company.
Both of these methods are great ways to finance a new car, and can be used to comparison shop against each other. My recommendation is to apply for direct loans prior to shopping for your car. Once you have a few approvals, you can pick out the best one (or two or three) and take those with you to the car dealership. Use those as a gauge to measure the dealership's offerings. (Read my article about how to shop for that new or used car).
In both types of products, you will need roughly the same information.
To apply for a loan you'll be asked for personal information such as your name, social security number, address & phone, employer name, address & phone, as well as your current income (usually gross). You may be asked to provide former addresses and former employers as well as a few references.
If you are applying with a co-applicant, that person will need the same information.
During the Loan Origination process the finance company will ask for certain documents in order to verify the information in your credit profile (this consists of your credit bureau report as well as the information on your application). If you applied through the dealership, the finance company will most likely provide a list of stipulations to the dealer, who will - in turn - ask you for the documents.
ID: You will need to provide some sort of government issued ID. Since you are buying a car, it is reasonable to assume that you have a driver's license, though a passport or a military ID will work for most finance companies.
Proof of Residence: If your time at current residence is short, or if your credit is not excellent, you may be asked to provide proof of residence. Your finance company should accept most bills (utility, credit card, cable TV). Some companies accept bank statements or pay stubs, but will rarely accept magazine subscriptions, personal mail, reminder post cards, etc. Finance companies do understand that sometimes the bills are not in your name (they may be in your spouses or parents name). If you are unsure about your proof of residence, contact your finance company and see what options they can provide.
Proof of Employment: This usually consists of a phone call to your employer. The finance company will simply want to call your job and talk to your boss, a receptionist, or another employee to make sure you work where you say you work. Make sure you have provided accurate information for this.
Proof of Income: The easiest way to provide proof of income is to submit your most current pay stub. In the first few months of the year, a finance company may accept a W-2 form. If you are self employed be prepared to provide tax returns for the past few years. If your income comes from a retirement account or annuity you may be asked to send in a benefits letter explaining your monthly allotment as well as how long you will be receiving this income (if you're income only lasts 2 or 3 years the finance company may not be comfortable asking you to pay back a loan for 60 months).
Proof of Insurance: You may not have added your new car to your insurance at this point (especially if you're still shopping). However, your current insurance usually covers you for 30 days after the purchase of a new vehicle. Make sure you bring your insurance card showing your coverage (this may also be required if you want to test-drive a vehicle).
Mortgage or Foreclosure Documents: If your credit bureau shows that your mortgage is behind or in foreclosure, make sure to bring the documents proving that you are current on your payments. Most finance companies will not lend you money to purchase a car if you are behind on your mortgage or if you have gone into foreclosure.
Bankruptcy Documents: If your credit bureau even hints at a bankruptcy, you will need documents to prove the current status. Usually the most recent court documents will be acceptable. If you are currently in bankruptcy, the finance company may not lend you money (as it is too easy to roll a new debt into a current bankruptcy). However, if you have been approved and your bankruptcy has been discharged, you may be required to provide proof.
If you have any special circumstances that affect your credit, residency, employment, or income be sure to bring any supporting documents you have when you go shopping for your car.
The finance company will most likely ask for other supporting documents (including the buyer's order, odometer statement, etc), but since they relate to the new vehicle, the dealer will provide them.
If you are buying a car from an individual, you will need to contact your finance company directly. Many of the documents required for that will differ from the list above.
In general, finance companies try to make this step of the auto purchase as easy as possible. Don't hesitate to ask questions of the dealer and finance company. Providing customer service is often the only advantage that some finance companies have. They'd be more than happy to explain each stipulation in detail.
Be sure to read my related article about the purchase of a new or used car or truck. There are plenty of tricks that the dealer's use and this article helps you avoid those pitfalls.