If it's feasible to ship the parts, they can be listed for sale online at sites such as Craigslist and eBay. Some of these sites can also arrange buyer pickup or local delivery.
Craigslist has a section in each of its city directories for the sale of appliances in which parts can also be listed. There is no intermediary for Craigslist sales as there is with sites like Amazon or eBay, so selling by mail is more risky. Craigslist is best for sales in which the seller is willing to personally deliver the item or is asking the buyer to pick up the item.
Any appliance parts can also be listed on eBay. The site has a dedicated area for them. Ebay listings also give the option of local pickup or delivery or shipping to the buyer.
It's also possible to sell parts by mail on Amazon, though it may be difficult if the particular part does not already have a listing on the site. In order to list a new product an identifying code such as a UPC or EAN is required, which an individual part is not likely to have. UPCs and EANs can be purchased from third-party sellers at an additional cost.