One little hiccup with running Emacs on Windows is that, by default, the spell checker does not work. The reason is simple enough, Emacs relies on an external program called ispell to do the spell checking work, and ispell is typically not installed on Windows.
Installing ispell isn't too difficult, though it's not trivial either. The first requirement is that Cygwin needs to be installed, or at least, the cygwin1.dll shared library needs to be somewhere accessible. Once Cygwin is installed, you can download ispell. See the README file for instructions. Do make sure to follow the instructions! Especially, do not forget to set the variable DICTDIR. It's easy with the instructions, but skipping a step can result in odd errors.
Afterwards, ispell can be invoked on the current Emacs buffer with the simple command M-x ispell.