Q: how do i back up my phone on someone elses computer

Hi leighfromca,
 

Thanks for visiting Apple Support Communities. 
 

If you want to back up your iPhone to another person's computer and then restore the backup to your new iPhone, there are a number of Support articles that will walk you through the process. 
 

See these links for the steps to back up and restore an iOS device:
 

• How to back up your devices using iCloud or iTunes
   
• Restore your device from an iCloud or iTunes backup
   

If you need to transfer iTunes Store purchases from the device (step 2 in How to back up your devices using iCloud or iTunes), you may want to create a new iTunes library on the computer before starting:
 

• Open a different iTunes Library file or create a new one
   

You may also need to authorize the computer for iTunes Store purchases. If so, remember to deauthorize it when you're done using that computer:
 

• Authorize your computer in iTunes - Apple Support
   
• Deauthorize your computer using iTunes - Apple Support
   

Finally, enjoy your new iPhone!
 

Cheers.