Learning key signatures all begins with learning the order of the sharps. If you like, it's "Fat Cows Go Down And Eat Buttercups". Then, after that, just a very few rules in using this magical list (the "circle of fifths").

During this tutorial I'll always keep the list visible, but it's a really useful thing to memorize.

The order of Sharps is F C G D A E B. If you are in a diatonic key (and you almost always will be) and there is only one sharp it will always be F. If there are three sharps they will always be F C G, and so on. Also, it will be important to know that if there are three sharps the last one is G, just as if there are four sharps the last one is D...always.