Heat some oil in a non-stick skillet over medium-high heat. Add the patties (you might need to do it in batches) and cook the first side for about 3-4 minutes, or until browned. Flip then cook the other side until browned and the sausage is cooked through.
The most reliable way to to check if a turkey sausage patty is cooked through is to use an instant read thermometer. The internal temperature of each sausage patty should be 165°F / 74°C.