Evaluate sin^-1 square root of 2/2

You could use the unit circle to find this. This could be something you have on a reference sheet or flash card, or its simply something you memorize.

Or you could draw out a 45-45-90 triangle in which the legs are sqrt(2) units long. Through the pythagorean theorem, you should find the hypotenuse is 2 units long. From there, notice that the sine ratio of either acute angle is sqrt(2)/2.

Or you can use a calculator. Many calculators have a button labeled or you might have to use the function which is the same thing more or less. Either is the inverse of the sine function, so it undoes what the sine function applies.