Most people picture cosigning as a character reference with a signature. The lender pictures it differently. On the contract, you and the borrower are two people who each owe the whole amount, and the lender gets to pick who to collect from.
Federal rules require a notice on a lot of consumer loans that says exactly this in one paragraph: you may have to pay the full amount, the creditor can collect from you without trying the borrower first, and the debt can show up on your credit record. People sign under it without reading it. Read it.
The loan lands on your credit report the day it funds. It counts against your debt-to-income ratio when you apply for your own mortgage or refinance, whether or not you've paid a dime on it. A lender looking at your file sees a $28,000 car loan, and "it's my nephew's" doesn't change the math. If a payment goes thirty days late, that late shows up on your report too, and you'll usually find out after the damage is done, because the statements go to the borrower.
Getting off the loan later is harder than getting on. The borrower has to refinance in their own name, which requires the credit they didn't have when they asked you. Some lenders offer a cosigner release after a run of on-time payments, often a year or more, and the borrower has to qualify on their own at that point. Ask whether a release exists before you sign, and get the terms in writing.
If you decide to do it anyway, do it like a lender. Get online access to the account so you see the balance and the due date yourself. Set up payment alerts in your name. Have the payment come out of an account you can see, on autopay. And decide, before the first payment, what happens if one gets missed: you pay it, and the borrower pays you back on a schedule you both wrote down. At the end of the day the lender doesn't care whose idea the loan was.
The alternative that usually works better is a smaller amount you can afford to give outright. A $3,000 gift toward a down payment doesn't touch your credit, can't go delinquent, and doesn't turn a family dinner into a collections conversation. Before you sign anything, run your own budget with the full payment in it as if it were yours, because on paper it already is. If that payment would sink you, the answer is no.