How to update to iOS betas using iTunes
As far as I could see it is not possible to download public beta's from iOS to your Mac. The only option Apple gives are OTA updates. 

You could register as a developer, but the beta's are only available for paying developers. 

If you are a developer, you can download beta's from developer.apple.com/download. 


Login
Go to the iOS section
Choose the right device
Download
Open iTunes
Connect iOS device
Click on the update button with alt (option) button pushed.
Select the downloaded beta