The LeapPad Ultra comes with a stylus. There are a couple of tether points on the tablet itself to attach the stylus to. Replacement styli can also be purchased if the existing one is lost, although the tether points do reduce the chance of loss.
The screen on the Ultra is a light touch screen, which is currently unique to the Ultra tablet in the range. This screen is designed to easily register the touch of a stylus, or even a fingertip, so it is very sensitive and using a stylus with it is simple.
If the screen does not appear to be reacting to the stylus, you must ensure that nothing else is touching it; because it is so sensitive, if part of the hand or body, or the stylus tether, touches the screen whilst using the stylus, it will detect that also, which can result in what appears to be a failure to read the stylus.