Have done it a bunch, here in the US. Best approach I found was to become totally calm (conditions premitting) and then move through at a speed that didn't compromise attention to detail- but not too slow, either. You don't want the baddies to anticipate your arrival at their precise location. Always be looking for something to get behind if need be, use any available cover and lighting to your advantage.
Rookies occasionally did two things that drove me nuts. They would either have the gun up in front of their face where they couldn't see squat, or they would make so much noise that a deaf person could tell where they were, and which way they were moving.
There's a lot to be said for sending the dog in, first.
“Nine-tenths of tactics are certain, and taught in books: but the irrational tenth is like the kingfisher flashing across the pool, and that is the test of generals. It can only be ensured by instinct, sharpened by thought practicing the stroke so often that at the crisis it is as natural as a reflex.” ~ T. E. Lawrence