Check the Vinyl Records Collectors Guide (VRCG) if you believe your vinyl records are truly rare or scarce. The difference between rarity and scarcity, as the VRCG defines it, is that rare records have a market. With scarce records, there may not be many of a particular pressing in existence--but demand does not exist, either.
Check vinyl auction aggregator sites such as Music Price Guide and PopSike to see what other people have been obtaining for the same records you have. These sites gather information on completed auctions from various websites (including eBay) and aggregate it into one centralized area for easy use.
Examine your own vinyl records carefully and be prepared to be honest with yourself about their condition. Even if the outer jacket or inner sleeve has a small bent corner from shelf wear that would not bother you as a buyer, it will matter to someone else in the record collector world.
Check your vinyl records for record company catalog numbers, country, and date of issue. Broadly speaking, original pressings are worth more than reissues. If you are ever in doubt about where and when something was pressed, finding a record company catalog number and searching it online should help to answer your questions.
Visit your local record shops and ask them to appraise your vinyl records. In many cases, you will probably be told that your vinyl records are not worth as much as you may have found online. Since you had the foresight to do some homework online, you may be able to bring this up and negotiate with your local record store, if you are interested in selling your records.