This is my Nidalee build that I have started using. I'm not saying it's the best build but I like it and I've had pretty good success with it. I tried a full AP build and it just wasn't working for me, and when I tried to go with an AD build, it just kinda became a hybrid. And I haven't lost a game yet.
Nidalee is fast, for running away and chasing enemies down. Pounce has a 2 second cooldown and you can spam it to escape or to finish off a wounded enemy who's almost made it away. You want to be careful as Nid until you get your ulti because without her cougar form she's a little vulnerable.
My build is a hybrid that starts out very AP centered but then I go on to build Guinsoo's Rageblade, which gives you both AD and AP, plus a nice Attack Speed and AP stack when you're fighting. By spamming Nidalee's Cougar abilities, you gain tons of attack speed and some ability power and this item helps you absolutely wreak havoc on enemy champions and towers.
It continues with Trinity Force for movement and pretty much everything else (which is why Trinity Force is one of my favorite items) and then the Hextech Gunblade for the AD/AP combo and the lifesteal/spell vamp to keep you healthy. And the 300dmg/slow active it has is nice too.
Black Cleaver is simply for more damage to destroy towers because at this point in the game you should be pushing hard to destroy their nexus, and it ends with Guardian Angel to keep you alive and bring you back if you can't escape.

Here's my last three games with this build, i'll post more soon

Nidalee is really fun to play. She's fast, deadly, and best of all, can carry a team and destroy towers.

Early game: (Levels 1-6)
You want to frequently use Primal Surge for the heal and the Attack Speed boost to stay in lane and get those last hits on minions. Stay alive and stay in lane, only throwing your spear if it will help you net a kill. Try to only use Primal Surge. Harass with auto attacks if you can. If the opportunity comes up to get an early kill, don't hesitate to try.

Mid Game: (Levels 7-12)
Mid game you want to go for kills, to try and get yourself fed use your spear to initiate a 1v1 encounter. After the spear hits, use primal surge for the attack speed then ulti and pounce on them, spamming your abilities to do damage and build stacks on your guinsoo's rageblade. In team fights switch back and forth between your human and cougar forms, healing with primal surge and attacking in your cougar form. Heal allies if they need it, especially your tank and any other AD carries you have.

Late Game: (Levels 13-18 and beyond)
Once you get some items built, you want to start pushing towers hard. Get your team together and push one tower at a time, using Primal Surge to keep your Attack Speed up and power your way into their base. Don't be shy about getting 10 or 15 more kills while doing that ;)

Pros:
Extremely mobile
Easy to escape from ganks
Easy to gank and chase
Has a heal ability, able to stay in lane long times
Can do tons of damage once built up

Cons:
Gets focused a lot in team fights
Burns through mana quickly
kinda squishy
Hard to master

For runes i like to go with some dodge and some defensive stuff, along with cooldown reduction to help you spam her cougar abilities and Primal Surge, and a little mana regen to keep Primal Surge usable.

For masteries I go 21-0-9 for the attack damage/crit strike but also some mana/health regen from utility.

Okay now here's the main part of the build. I start Nidalee out with a Doran's Ring for the extra health and that little bit of mana regen and ability power. This can help you net that first blood or at least a kill fairly early in the game if you play it right.

Second, I build Ionian Boots of Lucidity because the cooldown reduction is fantastic for Primal Surge, helping you heal up quickly, and her cougar abilities, which you need to spam while fighting (it doesn't affect pounce, though). Sometimes, if their team is really AP heavy or has a lot of CC (Crowd Control, like stuns, immobilizes, suppresses, etc.), I'll go with Mercury's Treads instead for that +25 magic resist and +35 tenacity. Magic resist also helps you tower dive which can net you a few easy kills on unsuspecting enemies.

The first damage item I build is Sheen. I like Sheen because it builds into Trinity Force, one of my favorite items, and it has this cool passive that makes any auto attack after using an ability do twice as much damage. When you are spamming your cougar abilities in a fight this means that most of your auto attacks are doing twice the damage. the extra mana is invaluable too, because you can burn through it pretty fast if you are constantly using Primal Surge (which you should because of the attack speed bonus, which helps you farm and get last hits).

After Sheen I build Guinsoo's Rageblade. This item is perfect for Nidalee because all her cougar abilities have relatively fast cooldowns and don't cost any mana. You can spam her abilities to initiate (primal surge, javelin, cougar, pounce, swipe, then takedown) and you suddenly have +24% Attack Speed and +36 Ability Power(plus another 50% attack speed if primal surge is fully leveled). You can also spam her abilities to get the attack speed boost when taking down a tower, and it'll be destroyed in no time.

That is followed by Trinity Force. I like to build Zeal first and then Phage before finishing off Trinity, but you can do whatever you like. Trinity Force is my favorite item because it gives you Attack Damage, Ability Power, Attack Speed, Crit chance, move speed, health, and mana. Everything you need to dominate a battlefield. It also has a passive like Sheen's (which makes sense, considering Sheen is part of it's build process), where every auto attack after a spell does 150% more damage. There is nothing this item doesn't do...

...except give you life steal and spell vamp, that is. So the next item I build is the Hextech Gunblade. It gives you massive amounts of Attack Damage and Ability Power (+60 and +75 respectively) and also gives you +20% life steal and +25% spell vamp, to keep you nice and healed up while fighting. If you can remember that it has an active that does 300 damage and slows your opponent, well, that's just an added bonus that helps you chase down your prey.

I follow that with a Black Cleaver, simply for the added damage and attack speed to help you destroy towers, because by this point the game has become about pushing and taking the nexus. It helps kill enemy champs too, which is always nice.

The last item is Guardian Angel, for the armor and magic resist to help keep you alive and the revival passive it has in case you can't quite escape.

My skill sequence is to max Primal Surge/Swipe first. The health it gives you and the attack speed bonus (50% at max level) is amazing for staying in lane and farming up. This ability is a must for Nidalee's success, and you should be hitting yourself with it quite frequently. It can also be used to save your teammates lives in a team fight if they get focused and can almost escape. You have to balance using your cougar form and your human form nicely, where you can pounce as a cougar but heal up as a human when escaping from pursuers. Swipe is also nice for farming because it hits multiple targets at once.

Second I max Javelin Toss/Takedown because that javelin can do some massive damage at long range. The damage goes us by as much as 250% depending on how far away you are.

Thirdly I max Bushwack/Pounce. You need one level on this ability before you unlock your ulti because it is invaluable for chasing and escaping. You don't really need to level it up until later after that though, as it doesn't do much damage.

Your ulti is Aspect of the Cougar, which turns you into a cougar, gives you some movement speed and dodge chance, and then gives you the other set of abilities. Obviously you level this at 6,11, and 16 like always for every ulti.

For summoner spells I like to have flash and ignite. Flash is invaluable, like pounce, for chasing people down and escaping sticky situations. Ignite helps you net some early kills when you don't quite have enough damage to kill them. Ignite will burn them away as they escape back to their tower and if you got them low enough they'll die despite getting away from you.

Other spells to consider:
Ghost is always good, you could go Ghost/Flash or Ignite/Ghost if you dont like flash.
Teleport is useful for ganks and tower pushes. If you are competent enough that you don't need ignite to get early kills, teleport is a good option for someone who has good map awareness.