Red has covered the basics. Not much to add, except I will relate how I typically approach a battle:
1) Run into a room
2) Pause the action (power wheel on xbox)
3) While paused look around for cover positions
4) Order team mates to cover positions
5) Release the power wheel (unpause)
6) Move to a position closer to the enemy than my squad
Never, ever let your squad use their powers on their own. They will not be available when you want them.
If you are good with the hotkeys/dpad, then you can use those to order your squad to use their powers. I am not so good with the dpad (I accidently issue a movement order rather than an attack command way too often) so I use the power wheel. I use hotkeys for Shepard's powers, but the power wheel for team mates. I have gotten used to pausing the game every few seconds. These pauses are usually very short so they do not really interrupt the flow of the action. The power wheel can also let you know if a certain power can be used against an enemy. Sometimes a mech or a husk might have a sliver of armor left on that you can't see in the HUD, but when you bring up the power wheel you will see that Pull or Slam is displayed as red, meaning they will not work.