Do not buy a used car seat unless you can verify the age and crash history of the seat, and can use the model number to verify that the seat is not under recall. You must also determine whether used car seats still have all of the original parts needed for safety.
Buying a used car seat means you are trusting the seller to give you information honestly. Can you trust a stranger on the other end of eBay to tell you whether or not that car seat was in a crash? Do you know the person at the yard sale well enough to know that they are car-seat savvy and have maintained the car seat according to manufacturer's instructions? When you trust a stranger to give you that kind of information honestly, you are essentially trusting them with your child's life, so it's important to make that choice wisely. My suggestion is to budget for a new car seat and cut costs elsewhere if need be.
If you have a trusted friend or family member who is willing to give you a used car seat, that may be a safe choice if you can verify all of the things mentioned above, as well as making sure that the car seat is not expired.
Car seat manufacturers set expiration times for their car seats. Some manufacturers even put a specific expiration date on one of the labels. Check the date of manufacture, which must be on one of the seat labels by law. Most car seats expire 6 years from the date of manufacture, unless there is a different expiration date marked on the seat. If you're not sure, call the manufacturer. If the labels are missing from the car seat, it's best not to use it, as the labels would also give you important model information that would alert you to potential recalls.
If you cannot verify all of the things I've mentioned here, the car seat is considered unsafe for use, even if it appears to be in good condition. Crashes can cause stress and structural weakness that isn't visible from the outside, and older car seats can be weakened by many seasons of heat and cold in the car. Unless a used car seat is coming from a close friend or family member and meets the above criteria, the best choice is to buy a new car seat for your baby.