Okay, so basically, I wrote this guide in order to get my head around Nidalee's mechanics. It's pretty much purely self-beneficial, but I figured that perhaps someone else could get a nice kick out of my ideas too (y) .

So far, I only have a whole bunch of math equations, and brief explanations as to what they are, but as I get more time, and perhaps increased interest, I may expand the guide to reach a user-viewing potential ^.^

Okay, so as i'm writing this guide, I tend to get lazy and neglect my proper spelling, and I like using abbreviations. Just in case you aren't sure as to what they are, I will display them here:

AD - Attack Damage
AP - Ability Power
MP - Mana points
HP - Health points
ArPen - Armor Penetration
MPen - Magic Penetration
Mresist or Mrist - Magic Resistance
Armour - I'm Aussie, and may sometimes spell Armor as 'armour'. This isn't a typo, just my language :P
Reduc - Short for reduction, lol.
Q, W, E, R - Ability corresponding to default hotkey associated. For example, to activate Cougar Mode, the hotkey is set by default to 'R'.
Quint - Quintessence, the best kind of rune for the specific tier.

I can't think of anything else that I may have used, however, it is late at night, and I am shocking in that I barely ever proof-read my stuff D:
So feel free to ask for clarification ^_^

Final equipment:

Ionian Boots of Lucidity
Lich Bane
Archangel's Staff
Manamune
Mejai's Soulstealer
Rabadon's Deathcap

Order of purchase:

Start with Long Sword + MP pot
Come back at 1345 gold, purchase a Tear of the Goddess, and Boots of 1.
Return at 1960, and upgrade Tear into Manamune, and purchase a Sheen.
Return at 1960 again, and upgrade the boots1 into Ionian boots, and then upgrade the Sheen into a Lichbane.

Purchase order gets rough from here onward. Buy a Mejai's according to how you are placed in the game. If you are dominating in minion kills early game, and you can purchase the Mejai's early, or you are getting lots of kills mid-game, then you should buy it. Otherwise, save the money and look at your scenario. If you are having troubles staying alive, buying a Rylai's Crystal Scepter will come in handy, as it will provide a level of slowing, as well as useful health, and the always-welcome 80 AP. However, if you don't think that this will suffice, and you are really struggling to secure champion kills, buy a Tiamat. It will provide useful HP and MP regen, as well as some bonus AD and splash, which will come in handy for skirmishing in Cougar Form.
NOTE: Tiamat's splash only affects nearby enemies by 35% of damage if attacks are ranged, so try to skirmish in Cougar mode for maximum effectiveness.
Now that you have your footing on the game somehow, whether it is wiping out waves of minions in a few seconds flat, or destroying entire teams in an equal amount of time, you should have the core of the item set. The Archangel's and the Rabadon's is really just icing on the cake. The Archangel's will give a lot more mana regen, so if you find yourself struggling for mana still, it's a good option, but it also gives a lot of bonus AP. However, if you're doing fine just the way you are, but maybe are struggling to stay alive, all I can say is to kill them before they kill you. That being said, the quickest way to dispatch the enemy, is through AP, thus, the Rabadon's. However, if you find that this is not enough, and that the enemy is just as fed as you are (hopefully not more D: ), then you might find, that a Zhonya's Hourglass will prove to be more effective. That extra 50 armor can prove to be a lifesaver, as well as a correctly timed Stasis Field. To add to that, the extra 100 AP is still going to kill them faster anyway.

Now that you have a nice position in your team, and are succesfully dominating in a field, you are free to smash your way to victory. If, however, the above build is not doing it for you, I am a major fan of mixing it up mega time :D
Try a Force of Nature if you are being dominated by spell casters, or if you are having money and mana issues, and need to heal your team mates (The health regen will mean less heal wastage on yourself).
Preferably, however, I like to play Nidalee in pubs, which means that I like to play very self centered. If I shoot for minion killing, I like to get atleast two tiamats, both lizard and golem buffs, and then just pick random lanes and hose down turrets whilst raking in cash. If, however, I choose to go the path of Champion ownage, then I lean towards the items that will benefit the following 'Javelin Toss + Lichbane proc combo'.

Once I have achieved Nidalee's full set of items, I usually stick to this solid strategy for wiping out enemies. Trust me, no one will ever try to demand a 1v1 with you again ^.^

Open with Primal Surge on self. This will allow for proc on Lichbane, as well as provide an attack speed bonus for 7 seconds. Neat synergy, huh? ;)
Auto attack target enemy to proc Lichbane.
Continue auto-attacking until little Sheen icon disappears (This means that you can proc the Lichbane again). Note that the attack speed benefits this auto-attacking.
Throw Javelin, which will allow to proc Lich again.
Auto attack to proc again. So much lovable damage! :D

Et cetera, et cetera. Nidalee is adaptable enough that she can suit any fighting circumstance. Enemy getting away? No problem.
Shift into cougar (R), pounce on/towards enemy, Takedown (Q), Swipe (E), then change back into human form (R) in order to heal/buff atk speed, and throw javelin again.

Enemy closing the gap between you and him, and threatening your health bar? Easy peasy.
Primal surge (E) on self for the buffage, cougar form (R), then mash a combo of Pounce (W), Takedown (Q) then Swipe (E) to remove some of that cumbersome health off the enemy. Depending on health situation, either repeat combo once again for more damage, or pop straight back into human form and buff/heal self again, as well as try and trap the enemy in a bushwack for 40% ArPen (A.k.a more Lichbane proc damage), and then a Javelin just for good measure. Surely by now you have the upper hand.

Any of the above happening and you're out of mana? Gets slightly trickier.
Activate mana pot straight away for increased mana regen, then pop into cougar form to mash W, Q and E. Once low on health (710 HP is low enough at lvl 18), pop back into human form to heal self, and then auto attack to proc Lichbane. Once the buff/heal and proc has taken place, wait until Cougar form comes back, and jump straight back into mana-less mode.

Seriously, Nidalee is super adaptable. There should be no reason as to why you cannot kill anyone once at full equip.

NOTE: In order to be adaptable, one has to have options. Nidalee has many options. Mana-less mode, AD spike damage, AP spike damage, heal, attack speed buff, ArPen reduc, YOU NAME IT. However, all of these options become useless once stunned. It would be important to try to keep clear of stuns. Sometimes I take Cleanse just for this, or, if I really am struggling, I sell my least used item (Manamune probs), and purchase a Quicksilver Sash (Has an active that's the same as Cleanse).


NOTE: That cooldowns on abilities will not carry over with shape shifts. For example, if you are in Cougar form, and you activate Swipe (E), you can shapeshift back into Human form, and within the cooldown time of Swipe, you can activate Primal Surge (E).

Nidalee's Stats

Javelin Toss

level 1
Without any buffs - 55 + (0.65 * 0)
= 55 damage (not including magic resistance)

With buffs - 55 + (0.65 * 20)
= 68 damage
Note: 20 AP is from amplifying tome.

(Veigar's beginning health is 355, Garen's is 455.)

Mana

level 1 - 265
level 10 - 670
level 18 - 1075

level 18 w/ fully stacked Archangel's & Manamune - 3065.

Extra damage from Manamune: 61.3
Extra AP from Archangel's: 91.95

Mana from full equipment:

Natural mana: 1075
Manamune: 1000
Archangel's Staff: 1000
Lichbane: 350
All up: 3425


Extra damage from Manamune: 68.5
Extra AP from Archangel's: 102.75

Lichbane proc damage

TOTAL AP:

Rabbadon's death cap: 155 + (50% of total AP)
Mejai's soulstealer: 180
Lichbane: 80
Archangel's: 102.75
Manamune: 68.5
Total: 586.25 + 50%
=879.375 AP

TOTAL DAMAGE:

Natural AD: 112
Manamune: 68.5
total: 180.5


Lichbane proc damage = AP + AD
= 1059.875 damage...

(ARMOR EXPLAINED: 100 armor gives 50% damage reduction and so 100% more damage is required to kill the champion.)

Armor vs lichbane proc:

93 armor - 48% reduced damage.
56 - 36% reduced damage.
Therefore, 1059.875 pure damage * 48% = 508.74 Recieved damage.

However, 93 - 18.26 ArPen (Provided by mark runes)
= 74.74
Bushwack at lvl 5 provides 40% ArPen, so 93 - (18.26 * 140%)
=25.564
Therefore, 74.74 - 25.564 = 49.176 Armor
Hence, out of the Lichbane's proc of 1056.875 pure damage, 25% will be negated.
Which leaves 792.65625 damage from the proc.

Total stats on Nidalee (w/o items, w/ runes):

Armor - 14 + (3.5 * 18) + 20.54 + 28.6
= 126.14
MResist - 30 + (0.75 * 18) + 48.6
= 92.1
Mana - 3075
ArPen - 14.94
MPen - 0
CdR - 0 (w/o golem buff, ofcourse)
AD - 126
AP - 0

Primal Surge (Heal + Atk speed buff)

Amount healed @ lvl 5 = 180 + (1.25 * AP)
Therefore, @ full equip, 180 + (1.25 * 879.375) = 1279.21875 health restored.
= 1280 hp.
Note: Nidalee only has 1990 at level 18.
Therefore, she needs to heal herself (1990/1280 * rounded^1.0) to be fully heal herself from 0 hp.
= 2 heals.
With a 10 sec cd, this would require 20 seconds, however, with Ionian Boots of Lucidity, end result of the cooldown would be: 2 (10 - (10 * 15%) )
= 17 seconds.
With the golem buff as well, the end result of the cooldown would be: 2 (10 - (10 * 15%) * (10 * 25%) )
NOTE: the golem gives 25% CdR maximum, it all depends on level.
= 12 seconds.
That's an extremely quick time to regain all of Nidalee's health. Plus, even better, if Nidalee begins healing herself when she is at 710 HP, she can fully heal herself in 6 seconds.

NOTE: That when calculating all of this, I stuffed up with the runes. I was under the assumption that you could get 11 runes and 3 Quints, but you can only get 9, so some of my calculations involving runes may be a little bit exaggerated >.<

Weeell, a few hours later and bloodshot eyes, I feel like this guide can be perused by you guys now ^__^

I hope you enjoy it, I put significant amounts of effort into min/maxing her stats to reach the best benefit possible. I honestly think that Nidalee is the most versatile champion out there, making her ace at pub-stomping, and still amazing in ranked games.

Please ask me to add in a section or clarify on something if you find that my guide is lacking. I would be more than happy to give an in-depth response ^.^

Supernatural Cow (Y).