By default, InDesign's spell check is manual. You go to Edit > Spelling > Check Spelling... and run the spell check on the selection or document. I had a student the other day wish that InDesign could put the little "squiggly line" underneath misspelled words like other apps do. And he was shocked to find out that InDesign already has that feature. It's called "Dynamic Spelling" and you just have to turn it on.
There are two ways to turn Dynamic Spelling on. You can activate it from the menu at Edit > Spelling > Dynamic Spelling. Or you can enable and customize Dynamic Spelling a little bit by opening the Spelling preference panel. InDesign lets you change the colors for different types of errors.
One note about the way InDesign works... You can only see the squiggly lines in the Normal view mode. If you are in Preview, Bleed, Slug or Presentation mode, the lines won't show up. This makes perfect sense, but I know lots of folks who design in Preview mode and they won't be able to see the squiggly lines.