Sell your records on pre-existing websites with a built-in clientele. Internet-based auction sites like eBay have become popular with collectors, and there are numerous online forums that deal in rare records that allow members to discuss, sell and trade their rare records.
Create your own website showcasing the rare records that you have to sell. This may not be a profitable endeavor if you only have a few rare records, but if you have many or plan on buying rare records to resell, this can be a profitable method.
Market your website to the right consumers. Even if you don't have a lot of money to spend on marketing, there are inexpensive ways to reach your appropriate audience. Forums and message boards dealing in rare records are an effective way to reach buyers. Ads in online or print magazines that target musicians can work well too, because many people that collect rare records are musicians themselves.
Consider putting your records in a consignment shop. Consignment shops take items and pay you when the item sells. This method can be satisfying for rare records, because it can be difficult to find a buyer for certain obscure records. If you do choose to go through a consignment shop, make sure they sell items appropriate to the era of the record or records you want to sell. A consignment shop that specializes in French antiques from the 1800s wouldn't be a good place to sell rare 1930s' jazz recordings.
Find a reseller that will purchase your rare records for a fair amount of money. Many independent record stores specialize in rare and uncommon records; they might be willing to buy rare records in a variety of conditions for a price that you negotiate. While this method may be simple and fairly quick, you should realize that you probably won't get as much money for your rare records as if you sold them yourself. After all, the stores are aiming to make a profit when they resell your records.