How does the credit union auto loans works?

They work just like a bank. Any lender (bank or credit union) will loan you the "loan value" on a used car that you want to purchase. They usually allow you to borrow the full amount for a new car. If you qualify for a $13k loan, but want to buy a $15k car, you have to come up with the additional $2k down payment. If you want to buy a $15k car but the loan value is $13k, you have to come up with the difference. Or you can bargain down the price to $13k.

Buy here, pay here financing is different, more expensive and riskier due to higher interest rates. Also, some of their cars have problems that make their selling price higher than what they are really worth. But other than that, they also work much like a bank or CU.

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RE How does the credit union auto loans works?

I apply for 13,000 auto loan with my credit union and was wonder how does it work.

Do I have to get a car for this amount or can I get a car for move say like 15,000

They lend you money; they get the title until you pay the loan in full.