The first part would generally be obtaining the certificate. You can use the official client ( certbot ), which is of course the recommended way, or one of the alternate clients.
You don’t need to turn off or stop your existing SSL for that.
Once you have the new LE certificate, then you need to install it. If this is a standard LAMP server, with no control panel in it - then the easiest is just to edit the apache config, and point to the new cert.