This is the electrical contact cleaner I used: http://www.amazon.com/gp/product/B003...
This is a permanent solution. The contact cleaner breaks down the crap (dust, etc) built up under your home button from all those years of use. Don't believe the other videos you see that tell you it's a software fix or the videos that tell you to wiggle a USB cable and magically fix it. Those "solutions" won't get rid of the dirt underneath your home button. This one will.
If you have any questions on what to do, comment and I'll see if I can help.