Burrows, latrines and 2-3 inch wide rub marks are all indicators of rats while mice will defecate as they travel and do not burrow into the ground. Either pest may produce nesting and correlated damage, insulation trails, or nocturnal noises. Rats will typically have a shorter tail and larger size. (See Biology)
While you certainly can try to remediate a rat infestation on your own, we do not recommend it. Rats learn from their experiences, meaning any failed attempt will make future efforts more difficult. It is ideal to enlist the help of a trained professional, and utilize whatever disinfection measures they recommend.
Decreasing ground clutter and harborage areas in proximity to your foundation is an excellent first step. Removing food and water sources will make your home or business less appealing, disinfection of pheromones at entry points, a rodent deterrent application around the perimeter, and ongoing exterior baiting are all effective elements to consider.