HELPPPPPPPPPPPPPPPPP! Spoliers!

Well in book two there is some kissing between them, but it is basically all Eric and Sookie is still with Bill. In book three they get a little closer. In book four Eric looses his memory and they have what you might call going out (they have sex all over her house) until Eric gets his memory back and forgets about "going out" with Sookie. After that they aren't together but there is a lot of tension in there relationship. Then in the last book out so far they finally get together more officially
They've never gone out on an actual date.

Hope that helps and I hope I didn't spoil anything for you but...it kinda seemed like you wanted it spoiled

Sookie and Eric don't atually "date", but they do become lovers in Dead to the World, the fourth book in the series.
This is, of course, why it's my favorite book in the series. :)