Glad to hear some positive words, I came in here expecting to see her get thrashed by public opinion. Diana is my favorite champion in the game, and a Champion I feel really strong on, Even when I'm a bit worried about how well i'll perform I've always done well enough, I've never been on her and just felt like I couldn't do anything to my opponent, and often feel pretty dominant.
This is my personal opinion, but I think if you're enjoying a champion you can do good on them despite the champion. So if you want to try someone out, do so. Especially if they show up on free week. I've found more champions I didn't think I'd like, but played them and enjoyed than I have the reverse.
Also as people here said and I've heard a few times now, the relation with her and Akali in style, Personally I feel if you put me on Diana I can do good, put me on Akali (whom most if not all would say is better) and I will be pretty underwhelming. (which is a lack of skill on my part, but it's more of an example how you can do better on a champion perceived to be weaker based on an individual)
I typically build her like Technomancer Jay's sustained damage though I tend to get a few of the "burst" items later on.
You can poke with her Q and farm some (if needed), sometimes at the same time. Being a curved skillshot her Q can hit in ways people aren't always as prepared for. Her W is a nice shield that allows you to trade pretty favorably when you're close up, and between her E and R she's really good at sticking to a target. And even if you use her Ult without getting the reset off it has a nicely short cooldown.
As MrBuffington said, she's on free week. Check her out and see for yourself.