The procedure is pretty simple and well documented in KB 321051, so there is nothing special here. However the tricky part is you have to submit the request from the same DC in order to make LDAPS work because this way ensures you have the private key for the certificate.
In some cases, it could take quite a while to obtain a certificate so you want to submit the request way ahead of time - so long ahead of time that you may not have the hardware yet at the time you have to send the request.
A workaround is to submit the request from another machine - any other machine as long as you make the request right. Once you get the certifiate, install it on the requesting machine, then export it with private key, finally import onto your new DC.