Hello and welcome to my AP nidalee guide.
The structure of this build is intended to be utilized at solo mid, but it could easily be adapted for laning with a partner.
Nidalee is an extremely durable character because of her healing capabilities. The reason that Nidalee will destroy your entire team with an AP build is completely based around the fact that she can lane basically forever (if you are careful), while harassing anyone who comes near very effectively. I would also recommend buying the blue pot whenever you have enough money to buy your core items when you come back but have 300 left over. Also, ALWAYS BE ON THE LOOKOUT FOR GRASS the speed boost is such a nice perk to track down someone or run away.
Ghost - ultimate for nidalee to chase down everything. NOTHING can outrun you basically.
Exhaust - makes getting close to nidalee even more dangerous, plus the added armor/mr reduction is awesome, AND melee champs like yi, tryn, etc can't just jump you and chop you down.
Flash - this could be taken because it could get you out of those sticky situations so that you can get away or position you for that takedown on the fragile and low hp champs. I prefer ghost though because you can close that gap with pounce pretty quickly but it lasts.
There are two items to select from when leaving for the mid, either a meki pendant or a doran's ring. I prefer the doran's ring because of the added hp, ability power (which gives you an extra 12 healing), and magic regen that rivals the meki pendant. The only reason that meki pendant can work well is because it will allow you to buy a tear of the goddess sooner. Upon reaching your lane try to last hit minions with your spear while tossing a couple at the opposing enemy. It is ok to take a little dmg in the process because you just heal and fire back faster, just be careful not to overextend yourself and as a result find yourself in a situation where you have to run because you have taken too much dmg and are thus in danger of being outzoned until you reheal.
Once you have enough money to buy level 1 boots and a tear of the goddess (and you are at least lvl 6 I assume) go shop. Here is the beauty of using tear of the goddess on Nidalee. Since she can change into cat form and use her abilities for free so she can basically farm mana at this point. Also, do not just run in with nidalee once you have cat form, you are still weak and can easily be focused down yet your escaping ability with Ghost and pounce is basically unrivaled. Nidalee is support and treat her as such, your job is to deal massive amounts of dmg from the sidelines, heal teamates, then jump in for the kill. When you notice the team battle has broken down the brunt of most of the champs abilities then jump in with Pounce->Claw->Takedown. With the added AP from masteries, runes, etc. at this point you should be healing like crazy with no fear of running out of mana anytime soon. Keep running around harassing mid and pretty much spam your abilities (especially cat forms) but don't go so far that you need to return to base if a team fight starts. You will need some mana to heal your teammates at this point. Nidalee's heal is so op and she is so fast that you can assist other lanes in trouble by ganking when they push too far. If you don't end up killing anyone just heal that lane's champions up and return to the mid to save your tower. Keep placing traps around so that you have LOS in dangerous areas. It can be so disheartening when a spear comes out of no where because you launch it at someone who becomes visible from walking through a trap. Timing is everything with your spear and it is VERY DEADLY at the end of its range. At this point you should have enough money to buy part or all of the zhonya's ring.
Once it is this late in the game you are keeping your teammates alive single handedly by just healing them for like 500+++ I find that when I get to around 30 minutes my heals can do like 1k. At the same time your spear should hit at the end of its range for like 1300++. It scares the hell out of the opposing team when my spear takes over half of a characters health at once or a champion is standing still thinking he is out of range with enough health then BAM dead (SPEARS OF DOOM!!!!) Just support your team by chucking spears, lay a trap, heal, then cat form rotation of pounce, claw, and takedown. Once finished change form rinse and repeat.
This is my first guide that I made pretty quickly but if you notice something wrong, have a question, or take issue with my build please post a comment so that I can address what you are saying. I have played A TON of games with nidalee as AD and AP but I love the team synergy you can get with ap because of the heals. The damage can still DEFINATELY be dealt with AP as well and you are more fitting to your role as SUPPORT.