I love playing Axis and Allies but think I have been playing it wrong. I place my troops on all of my properties. Is that wrong? Where are they supposed to start when I buy them? At the industrial complex, or anywhere?
No. New units can only be placed at industrial complexes.
From the rules, page 21, "Action Sequence 5 - Place New Units On Gameboard":
Place newly purchased land units and air units in territories where you have owned industrial complexes since the beginning of your turn-not in just-captured territories with industrial complexes.
Any units that cannot be placed in industrial complexes are lost and put back in the tray.
At the beginning of the game, units are started at designated spots dictated by the map, and by the rules (reflecting historical deployments).
As the game proceeds, land and air units start at one of your industrial complexes, while sea units start at one of the sea zones adjacent to one of your industrial complexes.
By definition, the industrial complexes are where your unite are organized and armed. That's why they start there (or in a neighboring sea zone).