How do I sync my new iPad air with my new iPhone 5

The should both be synced using iTunes with your computer.

How to use multiple iPhone, iPad, or iPod devices with one computer

Do you want to tether?

iOS: Understanding Personal Hotspot

http://support.apple.com/kb/HT4517

Use Bluetooth to tether your iPhone, iPod touch, or iPad

http://www.macworld.com/article/1159258/bluetooth_tethering.html

How to Connect an iPad to an iPhone Via Bluetooth Tethering

http://techtips.salon.com/connect-ipad-iphone-via-bluetooth-tethering-25472.html

Get a Mi-Fi http://en.wikipedia.org/wiki/MiF

 Cheers, Tom 😉