Look in activity monitor to see what you have running.
You will always have a little up and down internet traffic even if nothing is running because the modem has to keep in touch with the ISP so to say.
If you can´t find anything running, go to speedtest.com runs several tests and see what your speeds are.
If they aren't close to what your paying for, login to your modem, take a look at the DCHP client users table and see if anyone else is on your network that shouldn't be.
If all appears reasonable there, then call your ISP and tell them you're experiencing slow internet speeds and hope they can fix it.
Best of luck.