Replace the trimmer line on your grass trimmer with a grass and brush blade. This will be necessary to clear heavier grass.
Turn on your trimmer and use sweeping movements, from left to right, to clear low, heavy grass. This lets you clear the grass faster because you're cutting more with each sweep.
Use a single-sided movement to clear longer grass. This techniques gives you more power behind the swing, as well as more control.
Release the throttle on your grass trimmer when you have finished a sweeping motion. Then throttle up for your next stroke. This accelerates the blade and will drive even more power into the next sweep. This helps with particularly heavy grass.