You can order most of your forklift parts online these days, as long as you're aware of the part number and specifications. There are several distributors with large online catalogs and you can also buy them from other people pretty easily as well if you want to save money.
You can get forklift parts from a number of places.
First, there's Ebay. It sounds weird, but you can actually find a lot of used forklift parts on there, and even some new ones. You have to be a little more careful about the quality and the buyer, but it can be a good way to save money.
Second, there are a couple of online stores dedicated solely to selling replacement forklift parts. You can get a lot of parts here at ForkliftPartsDirect, but you've got to know what you want, because the descriptions aren't very detailed on a lot of the items.
Liftparts is another distributer online here. They carry parts for nearly every major brand. I also liked that they had a catalog entirely online that was easy to use. It's kind of buried in the site though - under products, then Literature.
HGM Liftparts is another one here that is a little easier to get around the site and catalog. They seem to have a better search option than the other two for finding replacement forklift parts as well, because it lets you search by keyword instead of just part number.