Diana is not a popular jungler, as she has lacking ganks pre-6 and high mana cost when clearing. However, once she hits 6, her power spike causes fear in the hearts of laners. When ganking, landing her q is the most important thing you can do. When Diana's q hits a target, their are stricken by a de-buff called moonlight. moonlight is special in two ways. The first way is that any champions hit hit by the skill shot will be revealed for a short time. The biggest effect is that if you ult on a champion stricken with moonlight, your ult will not go on cooldown. This ability is the sole reason why diana is scary, on the fact she can burst a champion with her ultimate being spammabl in a sense.
Tips

Always buy wards on every back, as junglers should be warding the second most of any role
Health pots are a must till Spectral Wraith is bought.
Land your q
Diana is a late game champion, so don't despair when you feel left out in early game fights
You may need it, but give your second/third blue buff and on to mid laners unless they are feeding, have no mana or energy, or you are being spoon fed kills
Prioritize stealing enemies' second blue buff so your buff can be given freely
Upgrade to Oracle's Lens when you have finished you first damage item and are warding often.