If you do something systematically, you do it in an orderly, methodical way. Someone who systematically records her dreams is careful to write them in a notebook every single morning.
Use the adverb systematically when you describe something that's carried out in a deliberate way, especially following a plan. You might systematically memorize every word in the dictionary, starting with A and working your way through the alphabet, or watch a toddler systematically pick up one Cheerio at a time from his bowl and throw it on the floor. Systematically and systematic come from a Greek root, systematikos, or "combined in a whole."