I've only done a couple, and I used an electric staple gun. I laid the grillcloth on a carpet and put the frame on top, then used those big binder clips that you use for thick stacks of paper to clamp the grill cloth to it.
It's fairly easy to adjust the grill cloth using the clips, when I get it straight and taut, I staple the heck out of it.
I've never managed to get one "factory perfect", but usually no one but myself knows where the flaws are.