Playing as Torbjörn
When a turret is placed on a health pickup, it is automatically healed when damaged while the health pickup is off cooldown.
When placing a turret down, try and place it so you will be able to repair it in a protected spot, such as right around a corner or hallway. It's more efficient for an enemy to attack Torbjorn himself instead of the turret when he is repairing a turret. This is because each repair restores +50 hitpoints a second. So try to take cover from the enemies when repairing turrets whenever possible.
Once you deploy and evolve you turret somewhere, join your team as a support fire if the enemy is not there yet. Don't understimate your left-click shoot. It has long range, is easy to aim and does fair damage. It can do some spare kills withouth having to get closer.
Once you swing your hammer while upgrading/repairing your turret, immediately switch to your gun and then back to the hammer. This will cancel the post-swing animation of your hammer and allow you to upgrade/repair faster.
You can use torbjörn's turret on the playload when attacking. This can lead to victory if opponents doesn't expect it to be there.
Torbjorn can drop armor packs for himself, but more importantly for his teammates whenever he has spare scrap, it's a nice way to support your team when you're already maxxed out your turrets.
Torbjorn's turret cannot see and handle everything on it's own. It's important for you to watch the back of your fellow Torbjorn teammates, because they're incredibly vulnerable to being picked off by the enemy team's offensive characters (including snipers like Widowmaker if he's not in an enclosed position).
Torbjorn's ultimate gives him a ton of scrap and armor to work with, so when you activate this ability, try to either: setup a turret in an offensive warzone position, rebuild a recently destroyed turret, or use it when your turret is under heavy siege by the opposing team because you repair your turret much faster than you normally would.
Playing with Torbjörn
Try to avoid picking up Torbjorn's armor packs if you're playing a hero with high base health like Roadhog. Lower-health heroes like Tracer or Mercy will benefit from 75 armor more than you. Only pick it up if there's enough armor for everyone.
When defending, be sure to protect torbjörn's turret if you have the skills to. A Reinhardt's shield would do the trick.
Playing against Torbjörn
If you hear "MOLTEN CORE", just grab a pint and wait until it blow over.
Widowmaker is great for taking out his turrets from a safe distance
It is often more efficient to aim for torbjörn first instead of his turret. Destroying a turret that cannot be repaired is an easy target.