Prepare
Doubles is such a quick game, I think preparation is key at intermediate levels. If you know what to expect, you can stay looser and think less, play better tennis.
At the net - cross court from the ball
This is your ball to hit. It is coming to you, know where you want to go with it. Stand in the middle of the court angles to make sure you can cover it. You should move slightly ahead of your partner, who should be at the net too, otherwise you are in bad shape and need to cover behind you as well as sharp angles in front. Strongly consider taking weak balls directly to your opponents, especially early in a match, tends to limit your opponents mobility later on.
At the net - same side as the ball
Protect the line by moving as wide as the ball is, a few feet in front of the service line. Be ready to take a nasty shot into your backhand, attack anything weak over the middle (unless low), and cover lobs if your partner is at the net.
At the baseline - cross court from the ball
Your ball to hit, decide how best you can get it back to the other baseline. If your partner is at the net, and the opposition is at the net on your side of the court, low and cross-court is the safest, followed perhaps by lob over their backhand shoulder.
At the baseline - same side as the ball
Position as wide as the ball, but expect to help protect the middle, especially if your partner is at net. Concentrate on were to hit to stay out of trouble if the ball comes your way, don't try and do too much from such a defensive position.
Stay low and focus on your opponents ball strike. Try to look loose and amused (especially if you aren't), it helps your partner and irritates opponents grim little heads!