Domain mapping multisite

Can anyone spare the time to walk me through domain mapping a site on a multisite network, if it is possible?

I have created a couple of sites on a multi site network, initially I was just playing about and getting myself used to things. They were test sites really, I never expected them to be used.

But I was asked to go ahead and use them. So, as I am new to all this I am calling on some help….

The issue:
I have 2 websites that were being hosted with pickaweb
I built 2 new websites on wordpress multisite (hosted on the same server as the original sites)
I have ownership of both of the domains, both already pointing to the server that wordpress is installed on.

The old websites no longer exist and I have redirected the domains to the new sites in their current wordpress domain format.

Is it possible to use the original domains on my now pre-built websites in the multisite network.

Apologies if there are a lack of details, I’m not sure what is needed. I am happy to add more info along the way.

I have seen a few online help documents but as I am new to this I wondered if someone could spare the time to walk me through the process?