This is a common problem that must be in someone's Access textbook. I've seen variants of this same question a hundred times in the last year. Since we aren't here to do your homework for you, I'll give you the overview of the approach but you will have to do the bulk of the work.
First, to determine whether a room is booked on a certain date, you need to have a table that contains a room number and a booking date start. If bookings can last longer than one day, you also need a booking date end in that same table.
Second, since a room can theoretically be booked more than once as long as the dates don't overlap, you need this booking table to not have only the room identifier as the prime key. Perhaps a booking number (Autonumber?) would be better.
Third, since a room might not be booked AT ALL, you cannot depend on keeping room definitions in the same table that holds the bookings.
Fourth, searching for booking overlaps involves multiple tests against the dates if you have multi-day bookings. You have to test to see whether the start and end dates of the proposed booking encloses the start OR end of the existing booking, and vice versa. If the bookings are single-day only, you can just test for equal dates.
Fifth, whatever you write has to test against all possible rooms (assuming you have more than one room that could be booked at the same time.) Therefore, failing to book room X is not a reason to say you can't book, if room Y also exists and could possible work as well.