How to Change TeXShop dictionary to American English?

The default language is the one chosen in the “Language & Text” System Preferences pane, where you can set the region to “British”. Or you can choose the language in the TeXShop Edit menu (“Show Spelling and Grammar”, that in the picture becomes “Hide”)

Go "Textshop" => "Services" => "Services Preferences" => "Text" Inside "Text" page, click "spelling" on the right.