Writing Truth Table Given Function
Write a canonical truth table with inputs x, y, z and output. Hint, it has 2^3=8 rows. Number the rows starting at zero and ending at seven. The output is one in the identified rows in the formula, and zero otherwise. If you understand the phrase "sum of minterms" you will understand why this makes sense. Look up what a minterm is, and the sum relates to Boolean algebra. 

Thinking in minterms it's trivial (though not especially efficient) to implement arbitrary Boolean functions of a handful of inputs using simple multiplexers, where the inputs are select lines and the mux inputs are connected to 0 or 1 as dictated by the truth table outputs.