Finding days past based on DS1307 Realtime Clock Module and Time library

I'm using the DS1307RTC Library DS1307RTC Library, For Accessing Real Time Clock (RTC) Chips in conjunction with the RTC module and the Time library. I'm trying to determine the number of days that have past, and I'm wondering what the best approach for doing this is. Obviously I can get the current day of the month and from that subtract the start day, but the complication comes with the fact that different months are different lengths. Is there an easy way to do this?

Days that have "past" since what? You are storing those values somewhere?

Outside of that, it's just math.
Make an array to store the number of days in each month, look them up & add together.

Is there an easy way to do this?

Fairly easy, and regularly done. I believe what you want is to find the Julian Day Number, which starts at noon GMT on Jan 1st 4713 BC, and you can work backwards to, or forwards from, there, thereby giving you days forward or back, days elapsed between dates, with all compensation, including the Julian calendar. This absolves you from any storage exercise. Standard works are by Peter Duffet-Smith and Jan Meeus.