Diana is one of those mid champs who counters almost every common mid champ one would encounter.
She has high burst damage, a shield which deals damage and grows stronger, a slow, and a practically cool down free teleport which also deals tons of damage. The only cons to Diana is that she is ranged, and has no viable escape ability other than teleporting to minions.

During the laning phase, you need to poke your enemy down to below half health, then jump them wih your Q, W, E combo. Get at least 3 AA to utilize her passive for max damage. If they are not dead by the time you have done this just back off for and let them burn their health pots. Use your passive to farm. Remember to always farm whenever you can. Just last hit minions. Poke them with Q whenever they try to heal to make their pots useless. But be warned: Diana is a MANA *****. A full Q+W+R+E combo burns almost half of our mana supply. So ask your jungler if you can have the Next Blue buff, or, be a boss and steal the other teams buffs.
Whenever the enemy is mia, push the last wave of minions and go roam. Diana's Q does enough damage to successfully gank any lane. If you do this, you will become so fed, you will see Diana become obese.

Your job during team fights is to go Rambo into the group of the enemy team and take out to squishiest champs first. Use Q to damage everyone and then Ulti to the most squishy target, pop your W and E, get out at least 3 AA then Q + Ulti to finish anyone who is low on health. Always run out of the group for your cool downs because without your abilities, you are useless!
Now if you find your self having to run away, don't run! Q + Ulti into whoever is low on health to kill them, then, keep running until you q is off of cool down then Q + Ulti into whoever else is low on health and keep running.

In conclusion, Diana is and OP mid champ who can only be shut down by other bursty ranged champs. I apologize if this isn't the most conclusive guide to Diana, but this is my first guide.
Thanks