Step-by-step guides will be hard to come by specifically for what you're wanting because not everyone will be using the same control panel if they are at all, but cPanel is the general choice here so we should be able to get something together for you, with the assumption you're using cPanel.
The first step will be to get your new domain to point to your server. When your server was first set up, you would have given us your first domain and should have set up your nameservers as ns1.first.domain and ns2.first.domain, where 'first.domain' would be that domain. You will need to set your second domain to use these nameservers as well.
Namecheap recently updated their back-end but they look to have done a good job of documenting it as well. You can find how to do this here.
After the domain points to your server, you need to set it up. I personally suggest creating a new cPanel account. This would be done from WHM (https://<YourServer'sIP>:2087/
) and can be done using WHM >> Account Functions >> Create a New Account. You can find more information about this here.
Now you can access cPanel as your new user at https://<YourServer'sIP>:2083/
and will install WordPress the same as your first account. If this was done manually before, WordPress's guide is a great resource for this and includes specific instructions for various panels.
If you're not sure if your nameservers were set up in the first place or are unsure about creating the account, you can open a ticket and we can check this for you. If you're using another control panel, we can certainly adjust this for your control panel.