How do i install on a new hard drive?

You boot into Internet Recovery, cmd-opt-r on startup. OS X: About OS X Recovery - Apple Support

From there, format the drive using Disk Utility as Mac OS Extended (Journaled).

Once that is done, exit Disk Utility and Install OS X.

If your Macbook shipped with installation DVDs, then you'll use those to boot and install.

Either method will install the original shipping OS that came with the Macbook. From there you can upgrade to El Capitan.

You can only download El Capitan from the Mac App Store, and you can only access the Mac App Store from an Apple computer/device. As it has been explained to me, you would need something that connects the hard drive to your Mac externally. Then you would need to go into Disk Utility, select the entire internal hard drive you have already installed (not just a partition of the drive, but the whole thing) and then select "New Image." You would then drag this new image to the destination drive, or the new hard drive you've connected externally. Afterward, you'd install the new hard drive and boot from that. As I said, that's how it was explained to me. Someone will no doubt correct me if I have any part of that wrong.

depending on the year/make model there are videos on how to add a HD

for instance a video for adding an SSD to a 2009/2010 MBP can be found here

https://www.youtube.com/watch?v=CHpK-w8bVns

the installation would be identical for an internal mechanical hard drive.

the above link is an EXAMPLE, not the procedure until you can identify the make/model/year of your mac

make sure you have the right mode, and exact year, there are differences between models and always use the correct tools and safety procedures. Laptops are easy to take apart but a nightmare to get back together if you go at this with the wrong info

Was the original hard drive defective? Did you remove it for that reason or did you just want to upgrade the hard drive?

You don't have to purchase anything. As stated by Barney-15E you have to restore the original os and then upgrade. The upgrade to 10.11 is free.