Don't let them see you sweat. When you start getting agitated, irate, a little red faced, flustered, blubbering, insolent, a little more quiet than usual, etc., I can tell, as your opponent, that I've got you on the ropes.
Now, you might think, "of course I know when I got someone on the ropes! It should be obvious by looking at the board!"
Have you ever finished that game where you though, "holy cow I was losing so badly and then all of a sudden my opponent did some things that caused me to win!" You turn around and ask the opponent and he says, "man, I was losing the whole time. Knew I couldn't win it so started moving some things around."
So, who was really losing the whole time? You or him?
When people feel like they are in a bad position, they tend to react a little more off center than usual. Heard of "flight or fight"? Well, it's not quite that primal, but when people feel like they are not doing well, they tend to make more mistakes, overlook things, and more importantly, give away tells. What's a tell? A tell is when you inadvertently give away information such as signals that you think you are doing poorly or losing.
There's a few things I can do with the potential knowledge that my opponent doesn't think he's doing well.
First, I'll become a little less risk adverse. I know that my opponent thinks that things are not going well and so will react a little more erratically, possibly missing key elements, possibly making bad decisions... you know... the kinds of things that make taking risks pay off!
Second, it also tells me that if I tighten the screws, I might be able to break his will and make him give up. Maybe I'll focus a little more effort on killing more units, giving the appearance of an oncoming tabling, and he'll just throw in the towel! Secretly, I can wipe the sweat off my forehead going, "IF ONLY HE HAD STAYED IN IT... WHEW!!!"
Third, I also know that my opponent's behavior is also about to become a lot more risky. He's much more likely to go for broke when he thinks he has no options left. You can use this knowledge to help you predict what he might do on the next turn.
So, what's the 40K Poker Face look like? The #1 key is to not let bad situations play on you. Lose your Land Raider on Turn 1? Respond with "On to turn 2!" instead of "oh, man, that screwed me bad! I hate my dice." Lose a critical combat? "Okay, on to this combat over here" instead of "oh man, I got screwed. I'm going to lose!"
No, the fake sportsmanship thing doesn't work on someone with half a brain for social skills. When you play off the "I'm acting super nice!!!!!", I can tell. If you can't tell, learn to tell. This is even better for you because your opponent will have a super hard time keeping up the charade when he thinks things aren't going his way. It's much better to be cool and calm.
Likewise, no, I'm not fooled by the "oh man I'm screwed .... (but secretly I'm not I just want you to make a mistake thinking I'm going to give up!) ....". You shouldn't be either.
Think either of the last 2 scenarios don't happen? I haven't been to a tournament yet where I haven't had at least one opponent actively try to engage in psychological warfare across the table top either feigning ignorance, acting overly zealous, feigning a loss, bullying for rules, etc.
It happens. So, use it to your advantage.