Surface Pro 3 by default has a Secured Boot UEFI-based system. So it doesn’t allow untrusted bootloaders which will help hackers to play with boot sectors. It was a great challenge to make a dual boot with Ubuntu.
So before starting things will be much easier if you have a docking station which will have USB ports, an additional Mini DisplayPort, ethernet, and charging.
Steps to follow:
Boot to Surface Pro 3 and disable hibernation as Ubuntu cannot mount drives that are in hibernation.
Now via Disk Management Shrink the volume of the drive.(If required disable Windows Defender and BitLocker both are known offenders for defrag operations.)
Now hold the “+” volume-key on the side of Surface Pro 3, then press the power button to load the EFI Boot menu-Select the Secure Boot Control option and set it to Disabled
Make sure you already downloaded the latest Ubuntu ISO to create a bootable USB following the instructions here.
Restart Surface Pro 3 and under the Recovery Options menu. Select the Restart Now button at the bottom of the screen, and on the following menu choose to Boot From Device –> USB Drive, to reboot from the newly minted Ubuntu USB drive.
On boot screen you will get the option to either “Try Ubuntu” or install it-better select “Try Ubuntu”
Select the “Install Ubuntu alongside Windows Boot Manager” option
You will find Type Cover keyboard doesn’t work and the WiFi is unstable
You need to download the latest drivers via Terminal add an entry to XOrg configuration to get the touch pad working on the Type Cover- you may need to apply a patch for driver support,which you can download to fix the problem.
Here is a detailed article on how to dual boot