download the
Windows 10 media creation tool and use it to make a win 10 installer on USB (on first page of media creation tool,m choose 2nd option which is make media for another PC, then choose USB or DVD (your choice)
if you doing a factory reset, just fresh install win 10 instead
You don't have to buy it again, when you upgraded from win 8.1 to 10 on desktop, you got a digital entitlement to always be able to reinstall win 10 on PC again.
Follow thsi guide for fresh install:
http://www.tenforums.com/tutorials/1950-windows-10-clean-install.html
when you reach screen asking for licence, click "I don't have a key" and win 10 should auto activate on install.