Did you realize that flats or sharps in a key signature always follow the same order? Lots of people are surprised to hear that, but it's true. If there is just one sharp in the key signature, it is always F. If there are two sharps, they are always F and C. Three sharps would be F, C and G. Four would be F, C, G, and D. The entire order of the sharps goes like this:
F C G D A E B
And you can always tell what key a song is in from the key signature by going up 1/2 step above the last sharp in the key signature.
The order of the flats is just the opposite:
B E A D G C F
Notice that the flats are in exact reverse order to the sharps.
To find the key in flat key signatures, look for the 2nd to the last flat, and that is the name of the key. If there is just one flat -- Bb -- then the key is F. And I'm sure you know that if there are no sharps or flats in the key signature, the key is C.
(Every major key has a relative minor key that shares the same key signature, but we'll consider that another day.)