I'm trying to change the site title of my blog to a TypeKit font- "Tangerine". I've installed the kit but I don't know how to actually change the active font.
I checked your Appearance → Custom Design → Fonts page, and currently you are using selected fonts from the 50+ Typekit fonts WordPress.com has built in to the Custom Design feature.
If you'd like to use different fonts from Typekit, first follow these instructions for setting up a kit using the advanced fonts option:
Once that is done, there are two ways to set a font. One is to find out what font name Typekit is using for the font you select and add that to your CSS editor with the appropriate selector (i.e. "ff-market-web-1" is the font name for the FF Market font you're currently using). But a better way would be to add the appropriate selector to your kit on the Typekit site. For the site title in the Shelf theme, you can use the selector "#header h1".
Typekit also has some documentation that may help you if you want to switch to the advanced fonts mode:
If you need additional help, you can also post back here with additional questions too.