Specifically, textfac.es (or textfaces or text faces) lets you finally write those damn unicode faces. The intended way to use it is as a bookmarked page in your bookmarks bar. When you need a textface, just hit the bookmark, click the face, and paste it where you want it to go.
The click-to-copy works through ZeroClipboard, which uses Flash (ew). If you've got Flash disabled, or it isn't installed, you'll have to highlight the faces, like a caveman.
If the faces look weird, or you see rectangles all over the place, you might not have the right fonts installed. Or the face might actually be weird.