I did a rough design of the sling shot in SolidWorks before starting the build. The frame of the sling shot is built out of black iron pipe. This was the simplest material to use, since I knew what lengths I needed and the hardware store threads the end of the pipe for free. The sling shot band is latex tubing, also available at the hardware store.
The pouch is made out of duct tape. I have tried other materials for pouches in the past (on other slingshots) like old towels, place mats, t-shirts, etc. But the duct tape has proven to be the strongest and easiest to fabricate.
To fire the sling shot, I made a quick-release out of some wood and a linch pin. The quick-release did not work as smoothly as I had hoped, but it got the job done.
Here is a video I made showing the sling shot "kicking" field goals.