Let me start by saying, reading the documentation and not just opening the page will often times help you with whatever your task is and save you, I dunno, 4 hours. Because this definitely didn't happen to me last week when I failed to read that linked clones need to be using one of these storages : raw, qcow2, vmdk format (either on local storage or nfs); LVM-thin, ZFS, rbd, sheepdog, nexenta.
Now that the warning is out of the way, docs :
As you can in the docs, this is rather straight forward. Ensure you have have one of the correct storage's note above setup. I used LVM-thin for no particular reason.
Once that is done, make a new VM as you normally would until you review the Hard Drive section. Here you must set your store to use your storage that we ensured previously was supported by linked clones. In my case my lvm-thin pool
After this set up your VM however you please. One done, shut it down. Then back in proxmox, right click on that VM and convert to template
Once converted to a template it will look like my 106 VM above. Right clicking on that will allow you Clone
This will bring up the clone prompt
Give your new clone a name and press the clone button.
Bam! You should now have a linked clone.