Im looking for some good advice on how to set up a good Item Build.
I've seen people talk about dedicating a rune page to make her effective early game.
Any advice on that would be appreciated as well.

7 attack damage reds, 2 magic pen reds.
9 armor yellows or health per levels, up to you.
9 ability power blues
3 ability power quints.

That and make sure to grab 3 attack damage from your masteries, and that will proc both passives. That's what I run, at least. I know some people choose to run ability power per levels on some of them but I'm more fond of flats.

if you have both passives you should start boots pots or amp tome pots and buy a hextech revolver as your first item. A lot of people chose to leave it like that and then build a Rylai's into a Deathcap but I tend to buy the hextech gunblade before starting the health part of the rylai's into a deathcap, since I like the slow and the extra ability in your combo chain.

Dunno if you need help in laning her etc but usually, keep your mark on them at all times while farming, and pop it if they try to harass you. This is especially prevalent top lane where they'll for the most part get within melee range to harass you. If you don't have someone who's a hard pusher as your lane opponent look to rotate a good deal and gank other lanes.

Hope that helped a bit.

AD reds, flat amour yellows, AP blues, and either health or movement speed quints.

Get the AD and AP from your masteries.

Since you'll be getting both procs on your passive, start with boots and 3 HP. Then:
Hextech revolver>Sorc boots> Rylais> Hextech gunblade> Deathcap> Void staff and if the game goes on long enough, another deathcap.

While in lane, always keep poking with your ranged ability whenever they get too close, and if they come in for the harrass, proc the mark on them. You can also use your ranged attack to last hit if you can't go in melee range.

After you get your ult, you go god mode. You're not un-killable, but you become EXTREMELY dangerous to be around. Throw your mark, ult on to them, auto attack, E, rinse and repeat. Remember that CC shut's down akali hard as she is squishy and a critting GP will rape you if you get stunned or snared by a ganker, therefore. To maximize your survivabilty, throw down your shroud and then perform your combo, you'll go invisible before they can retaliate.. Gank mid whenever possible.

Never. There are much better items than doubling up practically any item in the game; the three exceptions I can think of are trolling AAS builds, dropping boots for a second PD, and double Gunblade on Kat which might be obsolete from the passive change a month or two back. Obviously multiple Doran's items are useful, but I'm talking about endgame items.

I always grab a GA on assassins once the enemy AD has a decent amount of farm or a QSS if they have decent CC. But on Akali specifically, since she has such a high health pool and vamp/lifesteal, GA makes her that much beefier even without the passive.

You could always grab a LB for some extra burst and MS/MR which would far outweigh a second Rab.

You don't have a Lich Bane in that build.

1) Revolver is optional, beefing up your Vamp is useful but delays the rest of your build

2) Gunblade is very overrated on Akali, since the nerf. If you already have both passives, you'll burst harder and thus be better at what Akali does, if you invest in pure AP otherwise. Plus, it's actually ridiculous to invest even that much money in AD and Lifesteal if you are getting a Deathcap.

3) You need Lich Bane as much as you need Rylai's or Deathcap to unlock Akali's full potential.

I like to do like this:
MP Marks
HP/LVL Seals
AP/LVL Glyph
AP FLAT Quint

Masteries 21/9/0 (remember to activate your passive on masteries)

Build

Boots + 3 Pts
Giant Belt + Amplifying Tome (1520G)
*If come back before then Giant Belt + Amplifying Tome (1520G) --> Hextech Revolver (1200G)
Finish Rylai's --> Sheen --> Lich Bane

After that is really situational, I see Lich Bane as a MUST for Akali, her damage burst will be GODLIKE. Sometimes I like to get Gunblade before Lich Bane, mainly for it's passive, and because it's the only item that i usually get to give me lots of spell vamp (Attack Damage + Spell Vamp from Hextech Revolver).

Deathcap is not a Must for Akali imo.

LB is rarely effective on anyone as the first completion; usually you'd need around 70-100 AP before it becomes efficient to build. RCS is a better first completion because its passive allows you to do more damage to them as well as giving you more leeway for turret diving and overall crazy plays. However, building RCS, Rab, and LB means that you're skipping out on a Gunblade since your other items must be GA/QSS, Void Staff, and boots. If they're dumb enough not to build MR, then you can opt out of the Void Staff. Usually, it's a choice between LB and Rab, and I prefer Rab.

The earlier you get Lich (I go Rylai's > Lich), the more physical damage you will be doing as a component within your burst. This reduces the value of stacking MR, as well as the necessity of a Void Staff.

I usually play Akali pure AP to get as much benefit from Rab as possible (except for Gunblade which is hybrid). I prefer grabbing a Void Staff to make sure I'm still doing good damage into the lategame when most tanks have ~250 Armor to mitigate my AD Carry. I can see you grabbing a LB if your other solo lane is AP, but it's just not my preference I guess.

Mysteries and runes MUST proc both halves of her passive, you can do this however you want but IT MUST BE DONE and if you cant do this get a different champ.

I open with boots (turn this into sorc) and HP pots, first item i get is gunblade (because for some reason I'm OCD about having the active item in item slot 2), then death cap and lich bane.

I have 100+ games as akali.