Aleksandr, you can get a car loan at your local bank, credit union, or at a car dealership. It is a good idea to check with your credit union to see what you can qualify for BEFORE going to a dealership. The car dealer may or may not be able to give you a better deal than your credit union, but you must know what options exist or you will probably not get the best deal. Good luck to you.
Victor's advice is very good in this regard. I would like to add a couple of things from my experience.
I have found credit unions offer very good rates on auto loans, and some operate buying or search services to their members. These services are generally no cost to the member. Some credit unions (like the one I use) also offers lower interest rates on loans if their member uses the service.
Getting a loan through a dealer may be easier, especially for someone trying to establish credit. However, these loans may be higher priced (higher interest rates). The dealer will focus on the payment and will try to get you into something with a low payment, but it may be at the expense of a longer term (for example, six years instead of four years).
All this advice is good but I have to add something here. I have some clients in the auto industry and if you find the dealership group in your area that does the most business normally they have the most contacts and sometimes the best programs. My son financed his car through a credit union; however he was steered toward them through the dealership. Find a sales rep you trust at a successful dealership and let them help you. It never hurts to then take the information they give you and have another person with more experience than you look it over. The key is to find a sales rep with say more than 5 years at a dealership. Good Luck.
In addition to all of these good answers, here is a different angle; Is it possible for you to find a way to buy a car outright and avoid a loan altogether? I bring this up because I just went through this thought process for myself and concluded the following: I could by a car in excellent condition that is 5,7 or 10 years old. I don't understand the economics of buying a new or slightly used car. I went to Autotrader.com and ended up with a very nice 2003 Ford Explorer with 41,000 miles for under 9,000. It runs perfect and now I have no monthly payments! And don't need to worry about going over miles. (and don't stress out about dings in the parking lot) Admitted, it was more of a hassle than going to a dealer but I believe I did better financially. This route is not for everyone - each situation is different - but I'm convinced that one can get a car in excellent condition for as little as 7k if you are willing to spend some time and go directly to a buyer. . Best of luck! Evan