Psychological warfare is messing with people's minds, and making them think differently. Making people think differently or in a different manner makes them make mistakes. Makes them loose games. There are several ways of using psychological warfare against your opponent during a game of 40k, but I will say now that it is NOT bullying or physical. That is illegal. Psychological warfare in the 40k sense is about making the opponent doubt his decisions. Should he do that or this? This or that? Perform this strange art well and it will help you on your way to victory.
The Invincible Horde:
Possibly the most sub-consciously used psychological tactic of all. Simply having many more models than your opponent unnerves them. Help this along by saying they can't kill them all. They will shoot them all day and they still won't die. Stuff like that really helps to sow doubt in the targets mind. It makes him think again. It helps you. Obviously the best armies to do this with are Tyranids, Orks, and infantry high Imperial Guard armies. This tactic doesn't work much with Space Marines and small elite forces for obvious reasons.
The Invincible Elite:
For the non-horde armies there is also a tactic of making your force look invincible. Space Marines. "So what?" I hear you say? Well Space Marines don't have to worry about Tyranids as other armies as those genetically enhanced soldiers can beat the bugs in assault. Simple as that. Works well with Eldar too, zoom around with your grav-tanks and perform the usual irritating attacks. Make them look invincible. It helps make your opponent worry, and helps him/her along the way to loosing.
It's Big You Better Shoot it!
I like this one as it is one you can use to much better effect than the first tactic. The most obvious unit to use this tactic on is monstrous creatures. If you play Tyranids then this tactic is for you! It also works well with big tough tanks such as Leman Russ Demolishers and Landraiders. The aim of this tactic is to force your opponent voluntarily to fire a stupid amount of fire power to kill something. If you play Tyranids and have a big Carnifex with lots of guns. Make a big show of it shooting and squishing stuff. Make it look like the most deadly unit in the game. Brag about its past victories and stuff. Your opponent, if they take the bait, will then fire about half his firepower into that one unit. Having forgotten about the smaller bugs, the opponent now realises his mistake and prays for mercy. Give none! Just remember not to give theses "shoot us first" units really expensive upgrades as your opponent may get lucky and actually kill the unit. Never do this with a unit you know your opponent will kill (on average) in that turn unless it is to directly protect a much more valuable unit.
Do You Really Want to Do That? Really?
Just before the opponent points to which unit he is going to shoot at or assault, immediately ask him if it is a wise decision. If your opponent gets suspicious and asks why you are "helping" him tell him you are just being sporting. Repeatedly question his decisions; though don't go over the top as that's just immature. Be gentle, your opponent is human! Also as a more advanced thing to do suggest stuff not in a question, but as a statement. It makes it sound more final and as if it is the route to go down.
Make a Big Show:
Whenever you kill something, especially if it is something big and/or powerful. Brag about it a little (just a little) to demoralise you opponent. It can make the situation seem more desperate to your opponent who might make vital mistakes in an attempt bring the battle in his favour. Works well with making your opponent shoot the wrong unit in your army.
Just remember, veterans can be immune to this kind of warfare as they will know your armies capabilities and weaknesses. Also don't do too much that you stop the game or make your opponent quit. That's not in the spirit of the game, so don't do it. 40k is supposes to be a fun game don't make is a real war.