Connect your 3.7v battery to Ground (-) and +5V (+). The rated operating speed for the ATmega is (5.555 MHz/Volt) - 5 MHz (for voltages over 2.7) so a voltage of 3.7 would get you a speed of about 15.5 MHz. You could play it safe by running at 8MHz or overclock a bit by running at 16 MHz (the only two valid choices for Arduino).
I would not expect to get 3.3V from the 3.3V pin if you are running on 3.7V