Wai hello thar,
first off Diana is a good mid champion, consistant poke until level 6 and a huge assasin after lvl 6,...
NOTE: Diana is not a burst champion, she needs to stay alive and poke her enemies to win lanes, so cooldown reduction and mana regen in early game will mean a lot... get the 2nd or 3rd blue from the jungeler and try to win your lane.
Your build completely depends on your enemy:
if you're playing against a big poke like kassadin or cassio, buy boots and 3 pots and after that two dorans. Hug turret and farm until lvl 6 and then call for a gank
if you're playing versus a squishy champ buy doran ring (later buy boots of speed and kage's lucky pick) and poke them with your Q until they cannot farm (usually doran ring + masteries mana regen will give you enough mana to get them very low if you hit most of Q's) without being in danger of you killing them, push the lane and take wraiths/wolves and you will overfarm them easily
if you win the lane, and other lanes are neutral go ahead and buy rabadons after kage's lucky pick, you will be as much as assasin as akali, just keep farming waiths and take blue, poke mid until they go back, push lane and go gank,... hit the Q, use ulti as gap closer and E as an anti escape tool and your ganks will be successful
if loosing lane and other lanes are neutral you should go ahead and finish deathfire before rabadon, so if a dragon teamfight starts you can deal atleast some damage, concentrate on enemy team, you don't need to rush rabadon. If playing versus ad oriented team (top+jungle ad), buy zhonya after deathfire(maybe frozen heart as last item), and if playing versus ap oriented team (jungle+top ap) buy abysall scepter. It would be good to get rylai crystal scepter just so you have the bonus CC and the survivability with bonus health.
if other lanes are loosing, buy zhonya or abysall depending which enemy champ is fed
if winning just continue to buy usual ap items (you should have aleast rabadon, deathfire, void staff, rylai) and try to survive teamfights, be the last one in line and hit the q's, rush in when somebody is focused with your ulti
if loosing buy zhonyas, so if you get jumped on use Q and activate it,and by the time zhonya runs out you will be able to do another Q and activate W cause everybody will surround you. You should be able to deal decent damage before dying