I don't think there is any easy way to tell other than recording your IP address every day and checking for any changes. Many times if you have a dynamic IP, just by unplugging the modem, you'll get a new IP.
General rules, but definitely not guarantees:
If you have dial-up or DSL then you probably have a dynamic IP.
If you have cable then you probably have a static IP.
Fiber and LAN connections can go either way.
EDIT: Have you thought about asking your ISP?