This guide is a work in progress but I have included builds and some explanations of why I do certain things.

Between runes and masteries you will have enough AD/AP to activate both parts of Akali's passive, so you take Boots and 3 health potions first because the mobility and survivability helps quite a bit early game.

Poke and last hit with Q until you can get Hextech Revolver. Have your jungler hold the lane or you can kill your opponent(s) if you already hit level 6. If neither option is available, stay and farm some more until you can get your boots upgraded too.

Mercury's Treads - Generally these are the best boots to take in ANY situation, because of the valuable CC reduction. When in doubt get these, but if the other team doesn't have a lot of CC choose something else.
Sorcerer's Shoes - If you want extra damage or someone is getting magic resist to try and negate some of your damage.
Mobility Boots - If you feel like you need/want to roam a bit and help your team get some kills/assists.
Ninja Tabi - If the other team is almost entirely AD.

Remember to buy sight wards and Vision Wards every time you go back. If I can, I always get a vision ward to see if there are enemy wards nearby - if so, kill them ASAP.

At this point I generally rush Hextech Gunblade. I used to go for Rylai's Crystal Scepter at the behest of some other guides, but for the price it's just not worth it. Akali is very mobile and can catch up to (or escape from) almost anyone, so the slow (which is a very small amount anyway) is unnecessary. Gunblade slows, damages, and gives you a lot of survivability in addition to damage output - it's an extremely good item on Akali.

This is what I consider my "main build" at this point, and you build situationally from here. Doing well? Get damage. Doing badly? Get Chain Vest or Negatron Cloak. Not sure what to do next? Get a Giant's Belt.

I like to get Sheen (for Lich Bane or Trinity Force later) or Will of the Ancients next. Usually I get WOTA because your spell vamp will be insanely high and the aura benefits teammmates, but if the aura doesn't look like it will help enough of my team I won't get it. Needlessly Large Rod is a good option for when you're not sure where to go next.

Because having some CC helps your entire team, and Twilight Shroud hogs energy that could be used to burst people down, I've recently begun to get Frozen Mallet on Akali for survivability. It's kind of a luxury item but it doesn't do anything bad, and I like it more than Rylai's Crystal Scepter.

If I feel like trolling or backdooring I get Atma's Impaler after Frozen Mallet, and build a Sheen into Trinity Force. More often than not, Rabadon's Deathcap and/or Zhonya's Hourglass will be your next item though.

You absolutely need the attack damage marks and ability power quintessences for Akali; it's pretty much non-negotiable.

HP/level or armor seals are good.

For glyphs, here's where you have tons of freedom: flat MR, MR/level, or ability power are the best choices. I personally use cooldown glyphs because I already have a full set of the expensive bastards AND between the runes/masteries you begin the game with just about 10% CDR. It may not be a lot but it can help you out in tight spots where you wish you had an ability one or two seconds earlier.

Is 30/0/0 the best idea? No, probably not, but if you play safe then you shouldn't need 9 points in defense. I feel that I'm a fairly experienced Akali player and that the extra hybrid damage helps me out a lot in games. It's difficult to counterbuild hybrid champions because no matter which direction you lean in most they can still damage you; having 10% penetration for both armor/MR will be handier than you probably think.

Q and R first

W last

Done.

Your W is primarily for escape and tricking people, not getting the armor/MR bonus, and as I mentioned above it uses energy that could be being used for actual damage spells. So you only really need one level in it. You can do a lot of interesting things with Twilight Shroud though, so in certain situations you MAY want to actually max it over E. No matter what, prioritize Q and R first.

And because of W, building armor and magic resistance on Akali is rendered somewhat unimportant and you can just put a lot of health on her if you want survivability (keep in mind that you will have lifesteal and spellvamp to go with this!). It's similar to Leona's W shield in this aspect, but do not entirely neglect defense because Shroud has a long cooldown. Although you should play like an assassin, sometimes you get caught by the enemy. For the most part, just use Twilight Shroud in teamfights or iffy 1v1s to give yourself an edge in addition to slowing enemies.