First, you have to make sure your phone is in range if you are using a bluetooth connection and of course bluetooth must be turned on in your phone and watch. If you are using a Wifi connection instead, you have to make sure the watch is connected to the internet. You can check the connection status of both of these by going to the Settings option on the watch.
First you should make sure that the battery backpack is fully charged and connected properly to the back of the watch. Then you press and hold the home button located at the bottom of the screen until the screen lights up. If these steps do not work, please check the Samsung Gear S Home Button Assembly Replacement and/or the Samsung Gear S Battery/ Motherboard Replacement for more options.