Nidalee is an amazing pusher, has a great passive and so cool ultimate! Ultimate is the key of mastering Nida. The secret is to start harrassing with her Javelin Toss, adding movement speed with your Prowl passive and chasing the enemies while using Nida's ulti and Pouncing all the time.

PROWL (PASSIVE)

Moving through brush increases Nidalee's movement speed by 15%. The buff lasts for an additional 2 seconds after leaving brush. This is good for chasing and running away.

JAVELIN TOSS / TAKEDOWN

JAVELIN TOSS:
In human form, Nida tosses her Javelin doing big damage. In level 18, this ability will remove almost half of the enemy's health points! Use it often but not too often because it kinda wastes mana.
TAKEDOWN:
In cougar form, Nidalee bites the enemy. I reccommend using this ability when fighting against the Lizard or the Ancient Golem. It does a lot of damage.

BUSHWHACK / POUNCE

BUSHWHACK:
In human form, Nida sets a trap that doesn't expire ever. For example, Teemo's mushrooms expire after a few minutes. Nidalee's traps are immortal and they do continual damage to the enemies that stand on it.
POUNCE:
In cougar form, Nidalee jumps doing damage to the enemy she jumps on. This is great for chasing an enemy or for running away. It doesn't do very much damage but seriously very useful.

PRIMAL SURGE / SWIPE

PRIMAL SURGE:
In human form, Nida heals an ally granting it bonus movement speed. I reccommend to use this often because it is good when the 1 on 1 is getting even. Works just like the "Heal" spell.
SWIPE:
In cougar form, Nidalee claws at the enemies in a small circle. This ability is great for killing the minions around you.

ULTIMATE

Nidalee transforms into the cougar. Now, this is a bit tricky... I have seen a lot of players do a big mistake. They use human form more then cougar form which is absolutely wrong! In 1 on 1 matches be sure to start attacking with your Javelin Toss and in the rest of the fight be in the cougar form! The cougar doesn't need any mana and has extra magic and attack power. It is also great when running away from the enemy champions - Cougar's Pounce definetely will help you to chase down the enemy or successfully run away.

Starting with human form and ending as as a cougar: Q R Q W E R. Repeat. Good combo, mostly using a cougar form because abilities in cougar form DONT WASTE MANA!

Nidalee is a great champion at mid but only in LATE GAME. Don't start pushing mid early when you don't have your ulimate yet. Using your ultimate you can run away from enemy ganking and creeping at mid.

Nidalee is a support champion, good pusher with extra attack speed so make sure you add her tons and tons of attack speed with right items and runes. While editing masteries for Nida take mostly attack damage and some of the abilty power. Other ability power buy as items when the game is even.

EARLY GAME:
Pushing the lane and supporting your ally healing him.

MID GAME:
Pushing mid, team work.

LATE GAME:
Feed yourself! Gank a lot and chase with your cougar form so you can do more damage to turrets.