I am making an octagon and I want the width across to be 15 ft (diameter). How long should each side be?

Try drawing the picture.

The octagon will be cut into 8 equal peices.  each piece wil be an isosceles triangle.  The equal sides will be the radius and the angles in the middle of the circle will all be 360/8 degrees.  Use cosine rule to find the missing side.

Try it, if you have problems you can post again.