You may want to review multiplying polynomials first.
Squaring something just means multiplying it by itself. So, to square a polynomial, just multiply it by itself. For example, to square 2x2 + 2x + 2, you need to multiply 2x2 + 2x + 2 by 2x2 + 2x + 2, just like you did in the section on multiplying polynomials. (The answer, in this case, is 4x4 + 8x3 + 12x2 + 8x + 4.)
Some students are tempted to just square every term and string them all together somehow. This does not work!