Write down the function like this: f(x) = something, where "something" is the body of the function written in terms of x. Now, try to determine values of x that make the function undefined. For example, if the function is f(x) = 1/x, then x cannot be 0, since that would require division by zero. The domain of the function is all numbers except the ones that make it undefined.
Graph the function over the set of points in the domain. The range is the set of points that it covers on the y axis. For example, if the function is f(x) = x^2 + 1, then the range is 1 to infinity.
Write down the following equation:
f(x) = f(x + n)
Solve this equation for n. If there are no solutions for n greater than 0, then the function is not periodic. Otherwise, the period is the smallest solution of n greater than 0.