How do you kill weeds permanently?

That depends on what kind of weeds they are. If they are "broad leaf" weeds, you can use a herbicide like Killex that is for broad leaf weeds only. That means that it won't kill your grass. If it is a mixture of broad leafed weeds and grassy weeds, and you aren't worried about killing your lawn (as in you want to kill everything that's there), you can use a broad spectrum herbicide like Roundup. There are also soil sterilizers out there, but if you use one of those, be prepared that you won't be able to plant ANYTHING there and expect it to grow for at least a year, possibly more.