The easiest way to factor a polynomial, and the first thing you should look for, is factoring out a monomial. This is a simple matter of looking for everything the parts of the polynomial have in common. So, if I asked you to factor
xy + x2
You would start by looking at the two terms of the polynomial and noticing that they both have an x term. If you take an x away from the first term, all that's left is the y. Remember that x2 = x · x, so if you take an x away from it all that's left is the second x. This makes our factored polynomial
x (y + x)
Here's a more complicated example. Factor
x3y2 + x2y
Both of the terms have an x but we can actually do better. When you're looking for things in common you should always look for the smallest exponent. In this case, both of our terms have an x2 in common. If we take that out of both terms we get
x2(xy2 + y)
But we're not done yet. Notice that both terms have a y part. If we factor that out as well, we get our final answer.
x2y(xy + 1)
Notice that I left a 1 behind when I took the y out of the second term. That's because you can think of the original y as 1 · y.