Altogether means "completely" or "entirely" or "thoroughly":  "Her answer was altogether wrong.  She missed the point altogether."
All together means "in unison" or "gathered in one place":  "The choir sang all together."  "The books were placed all together in the center of the room."

All together is used only in sentences that can be rephrased so that all and together may be separated by other words:  "The choir all sang together."  "All the books were placed together in the center of the room."  See the usage note in the American Heritage Dictionary.

The simplest test is to see whether "completely," "entirely," or "thoroughly" may be used in the context.  If any of these words can be used, the correct choice is altogether.  If they cannot, the correct choice is all together.