There are two good ways to do the grill cloth either using spray contact cement or screen spline. Screen spline is easier, contact cement looks nicer. For the screen spline set your tablesaw to about 3/16" height and on the back of each grill frame saw a groove down the center of each side of the grill. Then buy some screen spline from the hardware store that fits tightly in the slot you just cut. Also round off all your corners and edges so you don't catch or tear the fabric.
Cut your grill cloth big enough to wrap the grill frame. On one of the sides, wrap the cloth around the back and insert the spline into the slot to hold the cloth in place in the center of the grill. Then do the same thing on the opposite side stretching the cloth some as you wrap it. Once you have the middle of both sides held with the spline, do the same with the top and bottom. Then I work my way around stretching the grill cloth evenly in all directions and inserting the spline all the way around. The hardest part is the corners, you can either fold them over or cut the excess fabric in the corners. Since you have a couple extra layers of fabric to fit into the spline slot you may need to enlarge the slot in near the corners to get the fabric and the spline to fit.