Always use a good sturdy tripod with a smooth video or birding head with fine adjustments to help you locate your subject.
If possible and your camera allows it - always use a remote or electronic cable release to minimise any motion blur caused by moving the scope or camera.
Try and maintain a fast shutter speed to help freeze the motion of the subject as well as reduce the risk of motion blur.
Avoid low light conditions - this will result in a slow shutter speed and a blurred image.