Start off with a new document of size 500x500 (or whatever size you are happy with, a square document will be better). Select Custom Shape from the toolbar and then Cirlce Frame from custom shapes.



Hold shift and draw the shape in the center of a new layer.



Draw two grid lines intersecting each other somewhere in the center. Position the circular shape in the center of two grid lines (the shape will stick to the center as you move it around the center, select Move Tool to move the shape). Now draw a rectangular selection as shown in the picture and press delete to cut the circle.



Now right click on the selection and select Transform Selection from the pop-up menu.



Move the reference point to the center (where the two grid lines meet) as indicated in the image below.



With transformation still active you will see transformation options on the top properties bar. Enter 120 in the rotation field and press enter. Press delete now to make another cut.





Repeat step 6 keeping the reference point in the center to make a shape as shown below.



Now use Elliptical Marquee Tool to make a circular selection, press delete to remove the brown area as shown below. Now right click on the selection and select Transform Selection from the pop-up menu.



Move the reference point to the center and rotate the selection at an angle of 120, press delete to remove the selected area.



Repeat the above step.

Now scale down the selection by dragging in any of the four corners (Keep Shift and Alt pressed while you scale down the selection, so as to keep the center and the shape intact). Fill the selection with selected color.



Rotate the selection by an angle of 120 and fill it with color.

Repeat the above step and you should have a unbuntu logo as in the picture below.