Introduction
Welcome on my build for Diana. The main concept here is to build up Diana with solide defense capacities without depleting her AP damage value.
I play mostly on Twisted Tree line, but I would use the same build on Summoner Rift.
The items build order is exactly like stated on the items build purchases above, with some modifications given the circumstances I would soon explain.
Pros / Cons
This build offer the following Pros and Cons to Diana:
Pros
+ Very good defence capacities in both field (Versu AD and AP)
+ High AP value to inflict serious damage
+ Early HP boost
+ Decent Magic penetration
+ Strong Burst damage
+ great mobility
+ Shield
+ Can jungle and lane well
+ No problem with mana
+ Can fight with range and melee
CONS
- Can be counter with Strong Mag Resistence
- No Cooldown reduction (but she doesn't need it absolutly)
- This build doesn't take full advantage of her passive (You would need attack speed)
Items
Why 
Haunting Guise rather than 
Rylai's Crystal Scepter? In short, to get the HP boost quickly without slowing the whole build items purchases progression.
You might say, get a 
Doran's Ring than, but it doesn't give you as much HP early and it will also slow you down by one better items. When I buy for first item the 
Ruby Crystal, my Diana get pretty tanky and I reinforce that by taking 
Pale Cascade for my first skill. Soon after, I can afford my 
Boots of Speed to get mobility. Then after, I get my AP boost with the 
Amplifying Tome. If you go for the Doran's Ring, in all cases, you will be one item behind. Since, I play mostly 3v3, the low cost of the Haunting Guise suite well that map, since the time lengh of the match is lower than in 5v5, so you have less time to gather gold for expensive items.
Another build proposal could made the Rylai's Crystal Scepter as core, but in this one, it is not the case. However, I think Diana benefit very much from an HP boost, since she is bound to get on the frontline. Given that, I need some HP boost without slowing my AP progression. This leave us with only two choices : Haunting Guise and Doran's Ring. The 
Rod of Ages is too expensive and offer a poor early AP progression, so I chose to not make the build around this item (Diana doesn't really need mana boost also).
Once you get the Haunting Guise, the other items are rather situational or, at least, given the "Normal" build, the items purchases order will be a bit different depending of the enemy team composition.
Basicly you have 3 possibilities:
1- The enemy team offer a good balance of AD and AP damage dealers.
In this cases, follow the Main build order. Since Diana need to get into close combat to inflict most of her damages, I prefer to buy the 
Zhonya's Hourglass first to get some resistence versus AD champions and auto attack.
If you still have a balance enemy team, but with a slight advantage on AP, than get the 
Abyssal Scepter first and after the Zhonya's Hourglass.
2- The enemy team is made mostly or only of AD damage dealers.
In this situation, by the Zhonya's Hourglass first and than skip the Abyssal Scepter. Replace it by the Rylai's Crystal Scepter. The HP boost from the Rylai will be reinforced by the armor from you Hourglass. This will give you enough defense. The Rylai boost your AP, so your damage output won't suffer from that choice, compared to one who would go for a pure defensive item like the 
Frozen Heart. After that, walk on to the 
Rabadon's Deathcap. Also, take the 
Ninja Tabi instead of the 
Mercury's Treads.
3- The enemy team is made mostly or only of AP damage dealers.
In this case, skip the Zhonya's Hourglass and get the Abyssal Scepter. After this item, buy the 
Lich Bane since it offer everything you would benefit to have a Deadly and Resilient Diana. The Lich Bane will improve even more your Magic resistence, it will boost your AP and also make your melee attack dealier. This scenario is the best given the main concept of this Build. Once you got the Lich Bane, continue your walk to greatness with the Rabandon's deathcap and complete the whole build with the Rylai's Crystal Scepter.
If the game last long enough that you can afford the whole build, sell the Haunting Guise for the Giant's Belt and buy the Rylai's Crystal Scepter. If you are in the situation #2 or #3, than replace the Haunting Guise by another item that would fit the circumstances. The 
Void Staff would be a safe bet.
If you face the situation where the enemy team build strong Magic Resistence, than buy the Void Staff soon after you get your first "defensive" core item (Hourglass or Abyssal). Get it before Rabandon, if they stack Magic resitence early. If you are with the Main build, that mean you skip the Lich Bane for the Void Staff and you still sell the Haunting Guise for the Rylai's Crystal Scepter.
Buy the Void Staff only if they get 
Force of Nature + one other Magic Resistence item. If they get only Force of Nature, your rune, Haunting Guise and Abyssal Scepter will give you enough Magic penetration to inflict good damage versus low or moderate magic protection.
Summary
I hope you enjoyed this build.
Your constructive comments, recommendations and critics are welcome. I take also praises and flatteries = )
On needs and given your comments and critics, I will improve the build.
Build Guide
Discussion
Nashor's Tooth, 
Malady and 
