To correct misspelled words (underlined with a dotted red line) simply hold down the 'ctrl' key while clicking on the word (or if you have a two button mouse, click with the 'right' button); this will bring up a box with possible correct spellings to choose from, along with other spell-checking options.
One tip: make sure you've selected, and dragged to the top, your preferred language (English, British English, Canadian English, French, whatever) in the 'International' section of 'System Preferences' under the 'Language' tab.
This is all easier to do than explain.
Cheers,
Tony