It's called completing the square. You need to have the form of (x-h)^2+(y-k)^2=r^2 for a circle. When you have unfactored variables, you have to get it into a form that does factor.
As long as the coefficient in front of the squared power (x^2 or y^2) is one, you take the coefficient in front of the x or y term, divide by 2 then square that. For your problem the coefficient was 1, divided by 2 is 1/2, and squared is 1/4. Since you added 1/4 you must also subtract it to keep equality. But now the x terms factor to (x+1/2)^2.
It just takes practice. It's not a hard operation.