gmail won't sync to my phone
Two things to check given GMail is already set to sync.

First, double check you have notifications ticked inside the GMail app, this can be found by opening the left menu and opening the settings located at the bottom.

Secondly, in settings open data usage, then open the three dot menu and ensure that "Auto-Sync Data" is on and "Restrict background data" is off.

Note: These directions are based on Stock 4.4, if they don't correspond just let me know what phone and software version you have.