Start by closing your right hand and stick out your pointer finger.
Stick your thumb straight up as though you were making the sign for a gun.
If you point your "gun" straight ahead, stick out your middle finger so that it points left and all your fingers are at right angles to each other.
If you have two vectors that you want to cross multiply, you can figure out the direction of the vector that comes out by pointing your thumb in the direction of the first vector and your pointer in the direction of the second vector. Your middle finger will point the direction of the cross product.
Remember that when you change the order that vectors get cross multiplied, the result goes in the opposite direction. So it's important to make sure that you go in the order of .