To spell check a word, simply hit M-$ while the cursor is somewhere in or at the end of the word. Ispell will check the word and allow you to correct it, if necessary. To spell check the entire document, enter M-x ispell-buffer. You can add words to your dictionary as necessary as you go.
Flyspell mode is the equivalent of that check-as-you-go spell checking that some word processors use, and is one of the features that proves you can have in a text editor the same features you have in expensive, proprietary word processors. Enter M-x flyspell-mode to toggle the mode on or off. Flyspell mode uses the ispell program to spellcheck your document as you type and changes to a different color all the words that appear to be misspelled. It only checks what you type from the moment you toggle the mode on, however. If you've already typed quite a bit and would like to flyspell all the existing text, once you've toggled on flyspell-mode, enter M-x flyspell-buffer to have ispell look over your entire buffer for spelling errors. If you get tired of the distraction of misspelled words (it's often better to just do all your spell checking at the end of the day instead of as you go, so you don't get distracted) you can toggle flyspell mode back off again with the same command.
Lots of good dictionaries have been developed for ispell, all of which you can download for free via your Linux system's package manager. Enter M-x ispell-change-dictionary and change the dictionary ispell will use for the next command. This is very handy if you use emacs for email and find yourself communicating in more than one language.