Audio/Visuals
SoundSound is a key weapon and defence in DOD. You should always play with the sound turned up so that you can pick out foot steps and other telltale sounds. With practice you'll be able to judge distances of footsteps and learn the different sounds on each map to track players' movements.
I play with headphones or with surround sound speakers. This allows me to judge directions with ease. With a decent soundcard and speakers you can turn around in the game and by listening pick out the exact direction of the sound, rather like a hydrophone (I was watching Das Boot last night).
Also all the weapons make very distinctive sounds and with practice you'll be able to identify each and every one of them and know whether the fire is friendly or not. Also listen out for other sounds like the chink the Garand makes when the clip is empty, the bleeding sound or the sound of a reload. These are ideal opportunities to strike as the enemy will be flustered - especially those bandaging themselves. Try to learn which doors make sounds and listen for grunts due to grenade throwing or jumping and with these combine them with on screen messages especially flag takings to track players.
Axis Sniper head to head with Allied SMG yet takes time to crouch and aim
rifle
Move and fire
Try never to move on your own unless you are trying to do some infiltration. Always move in at least a pair so one can run and the other is situated to give covering fire. Covering fire isn't random shooting it requires the second man to pick points where he thinks enemy fire is likely to come from and to fire at them if he sees any sign of movement, after checking the target is an enemy if FF is on.
By repeating this with roles reversed you'll be able to move swiftly with constant fire support and you'll be in a good position to assault any enemy positions you encounter. All movement should be done with a lot of input of the strafe keys to thrown off an enemies aim. Also remember using strafe keys you can move in one direction whilst looking in another, this allows you to keep an eye on likely sniper positions yourself so you are ready to take action if you see something untoward.
If you know the maps well enough you should be able to move around most parts, at least for short distances, backwards. This will allow two of you to move as a pair one covering the front and one the back and will help prevent any ambushes or the enemy sneaking in round behind you.
Sprinting
Sprinting must be used wisely in DOD as you can only do it for limited distances. Practice with the different classes so that you know exactly how far each will sprint, because there's nothing worse than running out of stamina in open ground. You should be sprinting from one piece of cover to another to cover longer distances. The ideal time to sprint is the wake of a grenade or artillery blast. There's a huge smoke cloud to hide you and by the time it disperses, if all goes well, it's too late for the enemy to aim and shoot at you.
If the distance is too great for you to make in one go and there's no cover my advice is to start off running normally until the distance is shortened enough to complete it as a sprint. This is because it always takes the enemy a short while to react, then they have to aim and in that time you should be able to suddenly accelerate out of their vision.
Also if you do misjudge and run out of stamina on a sprint I think you're generally best crouching for a moment and finishing the sprint. If you try to run it you end up hobbling along slowly and make an easy target that the enemy can pick off with ease. It only takes a second to gain enough stamina to sprint the rest of the way so ends up getting you there faster. Sprinting is also often your only defence if you're bandaging yourself. You are unable to fight back so if you are surprised try to avoid getting killed until you can retaliate