Here are the steps for going from 10 back to 8.1 from an MS support thread it should be pretty close to the same...
Make sure that Surface is shut down and plugged in.
Insert the USB recovery drive into the USB port on Surface.
Press and hold the volume-down button while you press and release the power button on your Surface.
When the Surface logo appears, release the volume-down button.
When prompted, select the language and keyboard layout you want.
Tap or click Troubleshoot,
Then tap or click Advanced Options,
Then tap or click Command Prompt.
If prompted for a recovery key - select Skip This Drive at the bottom of the screen.
At the command prompt, type diskpart.exe and press Enter.
Type LIST DISK and press Enter.
Type SELECT DISK SYSTEM and press Enter.
Type CLEAN and press Enter.
Type EXIT and press Enter.
Close the Command Prompt by clicking the "X" in the upper right corner.
Tap or click Troubleshoot
Then tap or click Reset your PC.
On the Reset your PC screen, choose Next.
If prompted for a recovery key, tap or click Skip this drive at the bottom of the screen.
Tap or click Yes, repartition the drives, and on the next page, tap or click Next.
Choose either Just remove my files or Fully clean the drive. The option to clean the drive is more secure, but takes much longer. For example, if you are recycling your Surface, you should choose to clean the drive. If you are keeping your Surface, you just need to remove your files.
Tap or click Reset.
Surface will restart and the Surface logo displays while the reset process completes (this can take several minutes).
During recovery, at American Megatrends screen, press Esc. (Not sure you will see this)
If the UEFI screen is shown, press Save & Exit.