I've got some experience playing nidalee, and she has two different play styles you can do her. I'm gonna show you how I do, what i build, why I do, and what you can change.

For the AP I get as much ap and magic pen I can. It's what works the best. Nothing more really to say here. If you want, you can take some mana regen runes, but I dont prefer.

For the AD I take dmg and I get some penetration too. Going a little tanky with the runes.

Basic masteries balanced between offense and utility. Mana regen from the utility is why i think runes are a waste, so with cooldown reduction runes. New masteries got it covered.

Basic offensive ad runes. with some defense.

The items are basicly just to get you some amazing dmg, but also to make sure you wont die in an instant with the zhonyas hourglass. Rabadons is a must on all AP carries, and so is the void staff on nidalee. She needs it. Spellvamp is just to make sure you can stay in there against the dmg making champions.

I find her really op with this build, she does alot of dmg with her Q. It is amazing to go in with her

This is what I use, to chase and get away, dont need ignite, the mid champ will take, and ad bot will take exhaust.

AD gets the exhaust and flash, for the 1v1 fights top.

I play her solotop. She is amazing at farming will do amazing dmg if you know how to, and when to. She can fail hard if you play her wrong, so be aware. Play carefully, but go aggressive lategame.

Play her aggressive with her range attacks, will scare the opponents.