Do you mean manually reprogramming the phone? You can't just put in a new SIM card and expect it to work, it has to be programmed.
You can enter that screen by typing in ##626*, then enter the code 587846.
Under NAM1, enter the new phone number under MDN. As for MIN, I'm uncertain what you would enter here, let alone SID. I would try searching for these items on the Web, under your operator. (Make note to save the previous information under these variables prior to changing them, in the event you're unsuccessful.)
I don't know what operator you're referring to, so I cannot advise you on what course to take, other than to call them and ask them what steps to take in order to switch your phone over to their service.