Decent smartphones have no issues finding GPS signals, and many now include GLONASS signals (Russian positioning satellites) as well. There are apps that require no data connection, just running on the phone. Garmin units are pretty good, and some of the newer ones, the 510 and 520 also receive GLONASS signals.

As far as counting, people were riding long before there was GPS, cell phones, and even electric cyclometers. Write down distance, duration and other relevant information in a notebook, or manually input them to STRAVA or whatever activity logging site or software you're using.