This is the same process as workers "clocking in" and "clocking out" as they enter and leave work. You are correct that you need a separate table where each record has a field for recording the timestamp that the person entered and the timestamp of when the person exited. (Timestamps record both date and time in one field.)
Here's some recent discussions of employees clocking in and out of a time card system that should be applicable to your library system:
Thank you very much for pointing me to the right direction. The solution worked like a charm!