You'll use anything with a 90 degree corner, such as a contractors square or even the corner of a sheet of paper to find the exact center of a circle.

Put the corner of your 90 degree tool somewhere on the circle. Draw a short line at the point where the two edges cross the other side of the circle.

Draw a line across the two marks you just made. This is the diameter of the circle, cutting it exactly in half.

Move the corner of the paper to another point on the circle (doesn't really matter where) and repeat the process. Draw across your two marks again. The center of the circle is where the two diameter lines cross.