Mansions of Madness is a very hard game for the investigators, so I am going to write from their viewpoint.
Get weapons. Don’t go out of your way to get them (you need to keep moving, see below), but you need a weapon as soon as possible. Switch with the other investigators to get an ideal one, but something is better then nothing.
Do not attack with out a weapon. Would you personally attack a zombie with your bare hands? No, you are only going to do it with an axe in your hands swinging for the fences. So don’t expect your character to do so. Run and evade if you do not have decent weapon.
Keep moving. Run when you can since moving to clue to clue is the most important aspect of Mansions of Madness. There is a clock in the game and you can tell when you are behind the ball.
Go straight to the next goal. This is not a Scooby-doo episode where you explore the whole house. You have limited time and you need to get to the clues and avoiding the monsters.
Stay together. This should be a standing order, however, there are times you can bend this rule.
Be careful of the wording on the clue card. The cards, from what I have seen, are literal room names. The first time I played this board game, it took me to go down the hall. So we went down a room that looked like a hallway, not know that there is a “room” called “Hallway”.
It is ok to die. If you are going to die, die quickly so that the Keeper can not use your weaken state for his own ends.
Typically, it is better to stay and fight a single creature rather then to run to the next room and suffer a horror check each time the monster chases you.
In Mansions of Madness, Skill tokens are hard to get so only uses them when the attack card has a large damage bonus.
As mentioned before this Mansions of Madness board game is a tough puzzle game for the investigators. Keep focused and say your prayers, because you might not get out alive!