How do I buy Team Fortress 2 items outside of the game?

Mann Co. Online Store

Once you make your first purchase, you get the Mann Co Online Cap (different from the Mann Co. Cap).

Since your post also references keys, you can also try Steam Marketplace. Think of it as a community market for the sale of certain TF2 items, and it's accessible from the main Steam panel.

http://steamcommunity.com/market/

While this may not be the only way, this is a way that works:

Go to this site, and scoll down until you see the "Contact us" box on the right hand side of the webpage. Right above it will be another, smaller box with "Supply Crate Keys" on it. Click the link, and you should be able to buy a key (Tested myself)

As to why the wiki site link didn't work, I would guess that the sites link is broken, possibly linking to a old store page