Let's start with buildings, as they are the best cover you'll find around you. Buildings are great cover, until a tank finds you and you're in a vulnerable position. Remember, try to get as high as possible to avoid getting caught by ground troops searching in the buildings, and aim your panzershreck towards the enemy tank as best you can. Grenades are also the focus of this next part. If at all possible, make sure to either avoid or throw back an enemy grenade.
If you cannot get away from an enemy grenade due to a wall or due to your location, try to get as far away as possible.
Finally, mortar is once again, your mortal nemesis in this game, much like tanks. Mortar when you're fighting in the tank section of the game can kill you extremely quickly. My advice to you would be to eliminate the enemy mortar team as quickly as you possibly can, that way, you don't risk being taken down by such an easily destroyed force.
Fighting with two weapons can prove difficult, but remember this simple rule - always keep on you two different types of weapon. For this game in particular, avoid the heavy weapons and keep to the mid-range weapons, as they'll always prove most effective in a variety of situations.
Always having on you a fully-automatic machine gun and the best ranged rifle that you can will serve you well as you get towards the end of the game. At all cost, avoid carrying around a panzershreck (with the exception of during a tank fight), avoid carrying a handgun of any type (too weak, and takes up a whole weapon slot), and even avoid the slower reloading rifles. Even though the default rifle is more powerful, swap it out for the Gewehr 43, as that particular rifle can reload even faster than the others.