Installation of OS after HDD replacement- Inspiron 15r SE

Since my HDD got conked a few days back, I replaced it with a new one.
How do install windows on this new drive? I do not have a recovery disk with me. 
My laptop (Inspiron 15r 7520) came pre installed with windows 8, but it had upgraded to 8.1 - I hadn't upgraded to windows 10. 

Can I simply download the windows 8.1 OS installer from Microsoft's website? From what I read, that  apparently does not work. What should I do instead??