This is my first guide, and I decided to make it for Nidalee on the Proving grounds, because I've had some success in ARAM's with this build and thought I'd share it. I wouldn't advise it on any other maps as it is mostly designed for people that want to throw spears as often as possible, and do as much damage as they can.
The runes I have given as an example are also the runes I use for general AP champions. The reason I think this works well with Nidalee here, is that the Greater Mark of Magic Penetration makes your spears hit much harder, and the extra Ability power is really helpful at giving your spears a lot of damage from the start of the game. Possible alternatives would be to replace the Ability power runes with Ability power/level runes, but this is personal choice.
Again, I bring general AP masteries for this build. The utility spells are really helpful here, and very important. You want to make sure that if you do die, you spend as little time as possible dead, as it can realy swing the game. Additionally, you want to have as much mana and mana regen as possible, in order to keep throwing spears.
I take Ignite and Flash on Nidalee. Flash in my eyes is very important here. The way I will play Nidalee with spears is quite passive - I try and stay out of the damage range and poke with as many max range spears as possible, however I use Flash if I want to get someone who is just out of reach without them expecting it. I.E. I will Flash forward to throw a spear and hit somebody who is behind their tower, who I otherwise would have been unable to hit.
here is possibly slightly redundant, but I find it very helpful in kill confirming. The only issue is that if you're trying to stay as far back as possible, it may not serve as good a use as something like Barrier or Heal.
is a good Summoner spell on all champions on the Proving grounds. I personally don't take it on Nidalee because she already has a heal.
is a possible choice for Nidalee, however this build is designed so that you shouldn't run out of mana too easily, at least not early on, and so you might find it rather unhelpful, or at least, you might find other spells more helpful.
is the final summoner spell that may be helpful to Nidalee. If you time it right, you can give Nidalee's Spears a big AP boost early on.
What makes this build different to other builds you may have tried, is the Meki Pendant.
The two Doran's Rings give you a high amount of Mana regen, a good amount of health, and obviously a nice level of Ability Power. You will find that you are slightly short being able to buy a 3rd Dorans ring at the start of the game. I've seen some Nidalee's wait the extra 20 or so seconds until they have enough gold to buy it, and this is a possible variation as it gives you extra AP as well, however for those that don't want to wait, the Meki Pendant gives you enough Mana regen to throw spears pretty much non-stop at the start of the game, and with the Magic Penetration runes, as well as all of your AP, your spears can easily get squishy champions to half health in one hit.
The first time you are killed, providing all goes well you should have a solid amount of gold. I get a Tear of the Goddess first myself, and if you have the money, the full archangel staff. The reasoning behind this is that if you are doing well, you won't be going back to buy items. That means that while you can still land damaging spears, the longer you don't die, the worse they are. For that reason, you may as well be stacking the Archangel so that you progressively get more ap the longer you're in the fight. When you're not spearing, switch to Cougar form and keep pressing skills every 3 seconds to stack the tear/archangels. It's free, so there's no reason not to do it.
Next time you die, I advise you to work on/buy your Rabadon's Deathcap. Should you buy it, the stacking Archangel will combine with the Deathcap to help increase your AP while you're still alive and gives you a hefty amount of AP too to get your spears doing the amount of damage you want them to. Boots early on have limited use in Proving grounds, however, if the other team have a Blitzcrank or a Nidalee themselves, you might want to get the Shoes as early as possible to help you dodge.
I've started building a Lich Bane on Nidalee more recently, my reasoning is that while Nidalee's spears are amazing, she becomes a little helpless in teamfights because of the lack of AD for her Cougar form. The Lich Bane gives you the extra damage you need with your basic attacks, and also provides you with more ap and some Mres for some extra survivability.
After these items, it's up to you what you build. I've found that most games end by the time you get these items, but obviously you need to judge what the other team are building. An Abyssal Scepter is always a good choice if they have a lot of AP (which most proving grounds teams usually do) And provides you with some extra AP and Magic Penetration. If your team is AP heavy, then getting a Will of the Ancients isn't too bad an idea either, although it might be better on one of the other members of your team. If you're feeling like you need a little health, a Rylai's Crystal Scepter will help with that, and will also help you slow people you hit with your spears. A Void Staff Can be better than the abyssal in some situations, as Nidalee wants to land spears from as far away as possible, and so the Abyssal Scepter may not give you any Magic Penetration for when they land. I reccomend the void staff if they build early Mres, as later on you're probably better with the Abyssal
Most people playing Nidalee will take Javelin Toss, Bushwhack and Primal Surge at the start of the game. While Bushwhack is very useful, I find it doesn't really come into play until later in the ARAM, when it can be used to find people to hit with Javelin Toss, and also to trap people running away. Therefore, I take 2 points in her Javelin Toss, as that's what we're going to be using most. I also take 1 point in Primal Surge, as it's very helpful for keeping you and your allies alive.
I try to max Nidalee's Javelin Toss as fast as possible, taking points in her Primal Surge when I can't level up her Javelin Toss. If you feel that you need more damage output, you can level up her Bushwhack more than I do, as it does do quite a significant amount of damage.
Throw as many spears as you can, and stay as far back as you can, and you'll be killing things all day long without being killed. (I've seen a Nidalee go 14,0,24 with the 3 Dorans rings Build, and my past 4 games with the meki pendant build have been - 11,4,14 / 5,1,4 (Short game) / 3,1,3 / 16,5,8)