Know your subject.
This is important in many ways of course, but in photography it will make your life easier and more importantly it will allow you to take better photos. If you photograph sport, know your sport and know the rules. This way you will be able to predict what is going to happen and capture the best moments.
Ok, I'm not super knowledgeable when it comes down to Deer but I know that during the rutting season, Deer and particularly the Red Deer, are very cocky - pun intended. They need to mate and they will show themselves in order to protect their space and their harem.
This is probably the best - and the most dangerous - time to photograph them in their full glory. Last weekend was a beautiful day and I was very lucky.
I may have said it before, but I love Dyrehaven. It's such a great park. It also has those gigantic wooden gates just like Jurassic Park. And at this time of year with all the sounds of fighting and growling it is an impressive place to be.