Wellllll, Albert=A, Bernard=B, here's the info they both know in chronological order:
1: A knows the month
2: B knows the day
3: A can't figure out the day
4: A knows B can't figure out the month
5: From the above info, B now knows the month
6: From the above info, A now knows the day
It may seem like useless information, but the 'trick' with these questions is knowing who knows what; they're never intuitive. Here's another example.
Okay, here's something to help ya start if you want to do it for whatever reason: there's only one day each with a day of 18 and 19; if B knew the day and it was one of those, that means he'd know the full date (i.e. if he was told "19" he's know the full date was May 19).
However, A knows that B definitely doesn't know the full date, meaning it cannot be May or June, since if he was told May or June, B could know the full date.
So A has been told July or August, and B has been told 14, 15 or 16 or 17.
That's the kind of thing you need to do.