there are various images for Galileo available - not sure which one you have installed.
You could setup Galileo as WiFi (or even Bluetooth) access point: Using Intel® Galileo as access point, or Bluetooth on Intel® Galileo - Bluetooth tethering | Intel® Developer Zone resp.
Or you could connect Galileo and your mobile to the same hotspot: WiFi access on Intel® Galileo with Yocto* Linux
You should find more docs on configuring lower level (i.e. wpa_supplicant) if you prefer to go that way
The simplest solution is to use the Connect AnyThing
Here is an article describing what it is:
Here is the github link: