How do I make my images sharper from my DSLR Canon EF 75-300mm f/4-5.6 III?

Set Shutter priority mode (Tv), set ISO to Auto, set shutter speed to 1/500th sec (the rule of thumb goes that you set shutter speed at least as inverse of your focus, like 1/300 sec for focus 300mm). There is not much you can do beyond that with this lens.