When do harry and Ginny get back together?

In the seventh, the Deathly Hallows.

When Ron gives Harry a guide to girls for his birthday (after they arrive at the Burrow - towards the beginning), he almost says that he's dating Hermione, but he gets cut off.

The book vaguely hints they are dating (they sleep holding hands when all three are in a tent, etc.), but Harry doesn't see them actually kiss until the battle at Hogwarts, when Ron says they need to save the House Elves.

They are married in the epilogue.

at the beginning of the series harry and Hermione have a love interest

Actually to the person above, I don't think they were actually dating until that kiss, they were just flirting. Also, Harry and Hermione NEVER had a love interest, as JK Rowling said many times they are strictly best friends, or brother and sister. It's always been Ron and Hermione and Ginny and Harry.