This is something I learned and geometry class and completely forgot for a while. All you will need is a drafting/drawing compass or a large homemade one for big circles. I have a little drafting kit that has came in very useful in engineering school! The steps are very short and will be best shown if you view all steps at once. Sorry if the pictures are blurry I don't have very good light to take pictures at my desk. Lets get started!
I'm going to use a piece of paper, since it will easily show the pencil marks, and draw a circle.
First, set your compass to just over the radius of the circle.
Second, place the pin end of the compass on the and draw an arc in the middle of the circle. I have made a big black dot where I placed the compass pin and will continue to do this.
Now on the opposite side of the circle where you placed the compass, create another arc keeping the compass spread larger than the circle's radius. You don't have to be exactly across from where you started as you can be fairly inaccurate to get good results.
Now we are going to make an arc perpendicular to the two we just made.
Now create another arc on the top of the circle directly across from the one made on the bottom.
Where two arcs intersect towards their ends you will need to draw a line between the two intersections.