Hello and welcome to my AP nidalee guide ,nidalee is a great champs who can farm in a crazy way after level 6 and can do tons of damage at mid-late game.
im not a pro gamer and im not a high elo player i just play for fun and i wanted to share my experience with you guys .this is my first guide so feel free to add comments and suggestions :)

Javelin Toss / Takedown - In human form, Nidalee throws a spiked javelin at her target that gains damage as it flies. As a cougar, her next attack will attempt to fatally wound her target, dealing more damage the less life they have.
Human: Nidalee tosses her javelin, dealing 55/95/140/185/230 (+0.65) magic damage on impact (deals up to 250% damage the farther away the target is).

Cougar: Nidalee's next attack deals additional damage based on how low her opponent's life is.

Cost
50/60/70/80/90 Mana
Range
1500

Bushwhack / Pounce - In human form, Nidalee lays a damaging trap for unwary opponents that, when sprung, reveals the target and reduces their armor and magic resistance for 12 seconds. As a cougar, she pounces forward, dealing a small amount of damage when she lands. Pounce is not affected by cooldown reduction.
Human: Nidalee lays a trap that deals 80/125/170/215/260 (+0.4) magic damage over 2 seconds, reveals the target, and reduces their armor and magic resistance by 20/25/30/35/40% for 12 seconds. Traps last for 4 minutes.

Cougar: Nidalee lunges forward, dealing damage to surrounding enemies.

Cost
60/75/90/105/120 Mana
Range
900

Primal Surge / Swipe - In human form, Nidalee channels the spirit of the cougar to heal her allies and imbue them with attack speed for a short duration. As a cougar, she rapidly claws enemies in front of her.
Human: Nidalee heals an allied champion for 50/85/120/155/190 (+0.7) and grants them a 20/30/40/50/60% attack speed for 7 seconds.

Cougar: Nidalee claws at enemies in front of her.

Cost
60/80/100/120/140 Mana
Range
600

Aspect Of The Cougar - Nidalee transforms herself into a cougar, gaining new abilities and increased movement speed in the process.
Human: Nidalee transforms into a vicious cougar, gaining 10/20/30 Armor and Magic Resist, 20 Movement Speed, and her basic abilities become Takedown, Pounce, and Swipe.

Cougar: Nidalee transforms back into human form.

Cost
No Cost
Range
20

Prowl (passive) - Moving through brush increases Nidalee's movement speed by 15%, which persists for 2 seconds when leaving brush.

Javelin Toss / Takedown :you need to max this skill after Primal Surge / Swipe if you need healing and farm or before it if you want ranged damage

1 2 * 3 4 * 5 6 7 8* 9 10* 11 12 13 * 14 15 16 17 18

Bushwhack / Pounce : you max this skill at last because your traps doesn't do a lot of damage till late game

1 2 3 4 5 * 6 7 8 9 10 11 12 13 14 * 15 * 16 17 * 18*
Primal Surge / Swipe:you max this first if you needed farming and health .

1* 2 3 * 4 5 6 7 * 8 9 * 10 11 12* 13 14 15 16 17 18

Aspect Of The Cougar:you take points in this as any random ultimate at lvls 6/11/16

1 2 3 4 5 6 * 7 8 9 10 11* 12 13 14 15 16 * 17 18

for runes I take Marks : Greater Mark of Magic Penetration :you are playing AP Nidalee so u need to have some magic penetration to do more damage

Glyphs: You have 2 choices here if u r going vs early game casters u use Greater Glyph of Magic Resist this give u some magic resist early game but if u have really strong all around the game casters u take Greater Glyph of Scaling Magic Resist this can give your magic resist all around the game .

Seals : I take Greater Seal of Armor Nidalee is a Squishy champion and she needs some survivability so she can last in lane

Quintessences : I take Greater Quintessence of Ability Power Nidalee needs some ability power to use her heals and spears more effective .

For masteries i go 21/0/9
IN OFFENSE:
1.i take 3 points in Brute Force which gives me attack damage
2. 1 point in Summoner's Wrath which improves ignite
3. 2 points in Mental Force which gives slightly more AP then i take
4. 1 point in Demolitionist which helps you attack towers even though you have low attack damage
5.then you take 4 points in Sorcery which gives you cool down reduction and that helps Nidalee Spam more spells
6.now u take 1 point in Arcane Knowledge the 10% magic penetration u take can stack well with Sorcerer's Shoes and Void Staff}
7.you take 4 points in Blast the 18 AP you get at lvl 18 helps a lot and gives you a small boost
8.you take 4 points in Archmage the 5% AP u get will turn into a good amount at late game
9. you take 1 point in Executioner and that gives a good boast for your AD which is a little low

IN UTILITY :
1. you put 1 point in Summoner's Insight that improves flash
2.you take 3 points in Expanded Mind which gives you great boost to your mana at late game
3.you put 3 points in Meditation and that gives you some mana regeneration and that is what Nidalee need .
4.you put 1 point in Swiftness which adds more mobility
5.you put your last point in Runic Affinity which increase the time of you using the blue buff and that is very important.

for items I always start with Doran's Ring because it gives me health and mana regeneration and that is what Nidalee needs because she is a really mana hungry champ in human form then I go for Boots to take some movement speed .

Guinsoo's Rageblade
this is the most important early game item for Nidalee it gives u everything u need ability power and attack damage and attack speed you just need to keep casting abilities in cougar form to maintain the Guinsoo's Rageblade stacks .

after that u need to upgrade your Boots and here u have 2 choices
1. If the enemy team has lot's of cc (stuns ,silence ,slow) you get Mercury's Treads the tenacity u get from them helps a lot
2.if the enemy team doesn't have a lot of CC u get Sorcerer's Shoes the magic penetration u get from them is really amazing .

after completing your boots u need to adjust your situation :
1.If you are using cougar form and close combat a lot u go for Lich Bane the 2 times ap u get on next attack is amazing then you go for Rabadon's Deathcap it gives u tons of AP
2.if you are not going into close combat and you are using spears more u get Rabadon's Deathcap first for AP and then Lich Bane .

after that you need more damage and magic penetration so you go for Void Staff} the 70 AP you get is really nice + the Magic penetration = WOW !

at the end u r going to sell you Doran's Ring and here you need to adjust the situation again 1.if u cant get the blue buff always get Morello's Evil Tome the AP and mana regain and cool down reduction is great
2. if you can get the blue buff always . you get Rabadon's Deathcap for insane AP or Zhonya's Hourglass for less AP and a little more armor .

i take Flash and Ignite this helps you get out off hart situations and helps you finish off low enemies
but there is other spells that work well :
1. Exhaust :this spell is good for chasing and reducing the enemy armor to finish them off quickly .
2. Heal this spell isn't used by on ap carries a lot but it can help you win fights and heal your team better
3. Ghost you can use ghost if you needed to chase enemies quickly or to run away but you don't always need it because you have Bushwhack / Pounce that gives you great mobility and your passive gives you movement speed when you walk through bushes
4. Clarity if you feel that you cant control your mana and you really need more get this spell it would help even though i don't recommend it.

Pros:
-Epic Spear kills and damage
-great farmer
-great mobility after lvl 6
-very effective heals when she has a good amount of AP
-really annoying to enemies when she farm well

Cons :
-Squishy
-No CC
-gets focused quickly
-Useless if she doesn't farm well
-not very strong against super high health tanks late game

Most of the times AP Nidalee is played as a solo top and the best way to play Nidalee good is to do one thing : ..... FARM !!! you need to farm in a insane way to get Nidalee to her best and after you get to lvl 6 it will be easy because you will have Aspect Of The Cougar + Primal Surge / Swipe which is a great farming tool of course you can still harass enemies but you need to focus on farming and after you get Guinsoo's Rageblade it should be easy and you can start to gank other lanes too .
TIPS: 1. try to always have the blue buff in team fights and in lane it can give you a insane boast
2. try to ward different places because u r easy to gank before lvl 6 and you can steal baron if you have a ward with Javelin Toss / Takedown ;) :P
3.when u r in lane don't try to get out of position and try to control the bushes u will have great movement speed in them
4. don't try to go 1 vs 1 against heavy tanks you are not so effective against them if you are not farmed well.
5.going 1 vs 1 against farmed melee AD like Tryndamere and AD Sion is a BAAAD Idea

Nidalee is a super champ when played well and she can do tons of damage . use her well and u will succeed.the guide is not done yet but i will try to finish it soon . add your suggestions and comments please :)