OLED Wrist accessorie

Hi,

I was able to upload the Adafruit SSD 1306 OLED Library to an OLED Display using an Arduino Nano.
Now I want to power the Arduino Nano via a Lipo Battery but the battery must be rechargeable and I already have a Sparkfun LiPoly Charger. The Sparkfun Lipoly Charger can use the System Out Header to power a 3.3v Arduino Pro.

Where do I connect the System Out Header from the Sparkfun LiPoly Charger to power the Arduino Nano with a 3.7v LiPo Battery?

An Arduino Nano is a 5V device. You can not power it with a 3.7V battery.

Well, you can connect the 3.7V to the 5V & Gnd on the Power Header.
Not all things may work correctly with less than 3.8V and 16 MHz system clock, like the serial port.