This is an "Instructable" about extracting Sunflower seed oil from homegrown seed.
You do need the mechanical extractor and while it could be home-built. I think in this case
it makes sense to purchase the unit.
http://www.instructables.com/id/Grow-Your-Own-Cooking-Oil/?ALLSTEPSThe extractor will also work on other oil-seeds, if you can grown them in your area.
Depending on your frame of mind, using non-GMO seeds may work better for you.
Please note the comment aoout "Black Oil Sunflowers" as being a better choice for oil production.
Other sunflower seed still produce oil, but in lower quantities...