Mid has become nearly impossible to win when playing against dull AP mid Diana. All you can do is try to farm and dodge her skill shots, which isnt much of a problem. The big problem that I have with Diana is her shield and her pull/slow.
-Her shield gives her a ridiculously strong shield both early and late game, making her impossible to kill with AP burst champions such of annie, ahri, katarina, anivia, and orianna. With the refresh of the shield, it can end up blocking any hard harassment from mid champions.
-Moonfall is even more op than Darius' pull before the nerf! She is able to pull everyone from ridiculous range. The op part about this skill is the huge delay before you can move again after she pulls. With the slow, this pull ends up being about the equivalent to ahri's taunt, except that it is on a champion that can burst you down within seconds.

Due to Diana's skill set, the only champions that counter her, besides champions suited for top or jungle, are heimerdinger, swain, and malzahar
http://lolcounter.com/search.php?search=diana

Learn to play Champions that counter her. Buy items that make countering her easier.

The thing about Diana is that she doesn't have a counter. She's a strong mid lane pick because she's very good and she doesn't have a true counter. There are just people that do better against her than others. Even Scarra thinks she might get nerfed a bit in the future.

Run Zilean. Seriously. The super heavy harass will push her out. And even if she tries to kill you, you don't die. Plus, if you get to late game, you can save whoever she blows everything on, nullifying her impact on the game.