I have a Canon Rebel T5i and recently purchased a sigma 18-250 mm DC Macro OS Canon lens. With the camera on and using the LCD monitor (not the viewfinder) the lens constantly tries to focus even while the shutter release is not depressed. Is this normal? And if not, how do I change it? I am new to this and any help would be greatly appreciated.
Some of the newer Canon EOS models, including your EOS Rebel T5i/700D, have a menu option named Continuous AF. With the T5i it is under tab 4 of the Shooting (Red tab with an icon that looks like a camera) Menu that includes most of the Live View options. If that option is set to Enable the camera will focus continuously as long as it is in Live View mode. To prevent the camera and lens from continuously focusing while in Live view set the Continuous AF menu option to Disable.
It's all on page 156 of the EOS Rebel T5i/700D Instruction Manual.
It seems your camera has touch screen, when you touch the screen it focus. If it only happens when using LCD, I'm just guessing, but maybe the screen is not clean and the camera thinks you are touch focusing. Try to clean the LCD Monitor with a clean cloth, even if you don't see it dirty, breath on it and clean it.