Overview of using SSL on your VPS

(Note: This was taken from a ticket response and needs to be cleaned up.)

You have two IP addresses assigned to your server. You'll need to assign the site wanting to use SSL to the second IP address (the first IP is your main "shared" IP). Go to WHM -> IP Functions -> Change Site's IP Address.

It will take four hours to update, you'll see a cPanel welcome page until then.

At the same time, you'll need to login to the domain's cPanel and generated a Private Key and CSR. Do this in CPanel -> Security -> SSL.

You'll need to generate the key first, then the CSR. When you purchase the certificate, you'll need to paste in the CSR into the order form whereever you buy it. The certificate issuer will send you the certificate or make it available for download. They may also include a certificate bundle / intermediate certificate.

When you're ready, go to WHM -> SSL/TLS -> Install SSL Certificate and Setup The Domain.
Paste in the certificate (all the text starting with

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Begin Certificate

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and ending with

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End Certificate

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), as well as the private key and intermediate certificates and click Submit.
Once the new IP address has updated and you ddon't see the cPanel welcome page for that site, test it out with https in the URL.

Note, that for SSL, only one domain can have the IP address. If you need multiple domains to have SSL, you'll need to purchase additional IP addresses and have them assigned to your VPS.