Search Internet sites that specialize in rare vinyl records, such as MusicStack.com or Gemm.com, to find a product identical to the one in your possession. This will give you an idea of how much vendors are currently charging for the record.
Contact a professional appraiser, such as Scott Neuman of Forever Vinyl. Send the details about the records in your collection and, for a fee, the appraiser will tell you what your record collection is worth.
Bring your collection to local record stores that sell antique vinyl. Let them know that you are looking to have the value of your collection appraised and you will not necessarily be selling anything immediately.