Multi pokemon battles are about pure damage and damage blocks. Nothing else matters. Every single pokemon you send out can and will die instantly if you let it because the enemy can easily use both his pokemon to smash you into the ground. Protect is vital. It's practically the only way to save your pokemon from dying.
This means status moves are almost worthless, especially toxic. Also, moves like leech seed and other stall kind of moves are all meaningless. This includes leftovers. Paralyze and burn are okay but more often than not, the enemy will just cure it with heal bell or some other healing move. If you try to stall someone out in doubles, the enemy is basically just getting free turns to kill the rest of your team. For the same reason, no one ever bothers with entry hazards. As you can see, anything that would stop entry hazards or status is completely worthless. Don't bother with magic guard or magic bounce.
In this, you want to replace leftovers with sitrus berry. You want protect on almost everyone. You also want lots of high damage or teamwide damage moves. If you have two pokemon you like to send out at the same time, give the one that's less likely to be targeted substitute. For example:
If you like to send out Blissey and Noivern at the same time, I guarantee the enemy will always try to kill Noivern first. So if Blissey sits behind a substitute, they will almost never try to kill her. This way she can spam out her healing waves nonstop.
As usual, priority moves are still incredible in this. Other moves to watch out for are rock slide, heat wave, surf, poison wave, and earthquake.
Lastly, figure out good combos. For example, sending out an earthquake user along with a flying pokemon is very wise. This way your earthquake won't kill your own team. Or you could send out a water pokemon and a pokemon with lightning rod. Stuff like that. Pokemon that are immune or love certain moves are very good. Flash fire, sap sipper, volt absorb, etc. Weather pokemon can work to your advantage if you have a good combo (e.g: Sandslash and Tyranitar). Pokemon with intimidate also do extremely well, as do anyone else that can affect whole teams at the same time.