Yes, when you go in a bank, there are the tellers, and then there is usually a place for customers who need services not provided by tellers, getting loans, certificate of deposit, access to safe deposit boxes, etc. So yes, you just go in and tell them you are interested in a loan.
First, take a look at your financial situation. How much are you making? What are your current bills/expenses? How much are you saving? You take your net income minus expenses minus savings. That's about how much discretionary income you have. Now, you don't want to blow your entire discretionary income load on a car note.

How much you want to spend on a car per month is up to you, but you want to leave some extra cash for things like insurance, title, registration, inspection, gas, repair and maintenance.
So, how much do you want to spend on a car? Do you have any money saved up? Let's just say there are cars in the $4,000 range and you want to loan $5,000 (hypothetical. It can be more or less). This amount will get you a car, plus, title, tax and registration.
You go to the bank and say you are interested in getting a loan for a car. They can get you two different kinds of loans. 1. A personal loan or 2. an auto loan. A personal loan will have higher interest, but you will own the car after the purchase. No lien. The repo man can't take your car, but they can get their money in other ways. Don't screw around with your credit history. You'll be uber-screwed when you want to apply for things that require a good credit history. Cell phone account, home loan, another car loan, credit card, etc.
An auto loan will have a lower interest rate, but the bank will possess the title until you pay it off. So if you stop paying, the repo man will come by. If you are approved, they will give you a check. You deposit that check into your bank account. Then, you can shop around for a car, haggle and make an offer. Now that you have your own financing, you can make low offers on cars (like $1000 to $6000 below sticker price), but not low ball offers, and possibly get a better price because you aren't getting financing from the dealership.
You can also just buy a car from a private owner (non dealership) because they may be willing to go lower on the price than a dealership. Like autotrader.com is a good website to check out.
See if you are eligible to become a member of a credit union. You may be able to get a better interest rate than a bank because you are a member.
But stay away from rent-to-own.