Mahjong is a game of matching tiles, so if you’re missing one of your tiles, winning can't help but become a problem. You can find replacements, but it takes a bit of effort because there are as many different kinds of mahjong tiles as there are manufacturers. Even sets made by the same company have variations in look, texture, thickness and color. While you may not be able to find a perfect match for less common sets, you should be able to find a tile that's a close enough match for play.
Contact the manufacturer of your set and find out if they sell replacement tiles; this is the best way to get the closest match. Unfortunately, companies go out of business or discontinue products, so this isn't a sure thing. Also, you may not know who made your set, so you'll need other options.
Contact mahjong organizations, such as the American Mah-Jongg Association and the National Mah Jongg League. These groups bring together mahjong players and collectors -- some also offer tile-matching services and provide a forum where you can buy, sell or trade tiles.
Browse online auction sites after you've talked to the manufacturer and collectors to ascertain the value of the tile you need. Mahjong tiles appear on auction sites often enough to make them worth checking, but it's up to you to ascertain a fair price.
Look through listings from private buyers and sellers, such as the Mahjong Tile Replacements & Museum or The Maj Exchange. These types of places and websites either represent private sellers or serve as a sort of “classified ads” for mahjong tiles and sets.