Remember, you have two choices with Nid:
Attack Damage, or Ability Power.
Now, AD has the following benefits:
a) Totally pwns AP Nid, but you can't mirror in ranked games
b) Pushes towers faster
c) Generally 1v1's, since that she has an AMAZING attack speed boost, and if goes to a point where you're both low, she just goes to R and then Q's you. 900 dmg, FTW!
AP Nid, on the other hand
a) Can save people's asses
b) the Damage scales with her cougar spells, making them more useful
c) Because AP makes her cougar spells stronger, and because her spells are AoE, she does more damage overall
d) It's funny to throw a Q from far off into a Teemo's face, and he dies.
e) Is not much of a 1v1 champion. Because she gets pwnt by her AD Counterparts.
AD: Boots, Phantom Dancers, Infinity Edge, mhmm...
Basically, just make it so you have one less AS item then you normally would.
Her heal spell takes care of the missing attack speed.
AP: This varies alot.
I can start off with a Ability Tome (I rush Mejai's alot, because my Q spell disallows running away and kills people from far off)
Then, of course, Mejai's or Boots, Zhonya's, Rylai's, Rod of Ages, Lichbane..
Just keep in mind: For AP Nid to be of use, she has to use her spells (D'oh! So that's what I've been doing wrong!). However, her cougar spells have a small AoE. Thus, she has to go to battle. I usually never skip out on Rylai's, and Rod of Ages is an often pick.
She wastes alot of mana. It sucks. =[ Pick up Clarify if Doran's Ring isn't enough for you (I actually get Doran's on AD builds as well) Or lane with Soraka
Cougar Mode W is a mini flash. Use it to run away. In some walls in TT, you can jump over there if you're at the right angle, but that requires practice.
NEVER EVER PICK UP THE SPEAR FIRST. Always get BUSHWHACK.
Why? Because lvl 1 spear SUCKS. Nidalee is not first gank material. Out of all her spells, Bushwhack is the best choice, because you can spam that around, allowing you to be prepared for early ganks.