two versions to diana
tanky ap, and full burst ap.
you can go
(dorans into roa, or double dorans into zhonyas whichever is more needed)
or you can go bursty
(ludens may be replaced for zhonyas for sake of survival, but ludens is better burst/movement)
(double dorans into abyssal -> lich bane, and boots when applicable)
i personally prefer burst for just maximum damage, ill go in when its favorable, however the enemy may never give me the option and ill probably be useless or forcing my way to the back line.
the best way to play her is towerfarm till 6, because you dont have a gap closer, focus on getting farm. hit 6, hopefully have a sheen, and dive onto someone without any MR and it should be enough to kill them. you push your wave and roam against someone pushing or whos all alone.
and as always, try to land Q's for ult resets, but its fine to use your ult outright if you think you can get the kill anyway.
while in lane auto twice to get your passive ready and then go in, its a noticeable amount of damage difference in your combo.
i do not recommend jungle diana, i just dont think its viable, you need someone who can front line and diana just isn't it, she is an assassin.