Many others have said it, do your research. There are many websites that will give you a range of prices for what your record(s) might be selling for.
Some of your old records (if they are in good shape) could be worth quite a chunk of change. Sadly, it can be a little time consuming, but it's fun and worth it if you have a little time. Often, if it's a rare record in great shape, you will get the best return by putting it up for auction on eBay but this is also time consuming. If you just want to get rid of them quick and want a little money, give your local record store a call and see if they want to buy them.
If you do decide to auction, pay attention to the record grading, carefully clean the records well and take good photos of the record and the sleeve. If you have something special; like a promotional copy, colored vinyl or a first pressing, make sure to mention this in the description. If you have additional information about the artists or the release, include that as well.
Good luck!