I'll bite. This is a big question honestly lol.
Since you are non-radar, the relay folks need to transmit you data and plot it. I'm keeping this on a basic level. Yes, Most mainstream airlines/modern planes use ADS-C, CPDLC, and are FANS-A1. Using HF and Satellite comms to communicate position across water. I'm not really up to speed on real world NAT Track stuff sorry, but the rest of the World hasn't really changed. Different parts of the world do reports and coms different as far as lingo.
Blast off, make a coast out fix at altitude. The controllers are going to want to know Flight Level and Speed in Mach. Be at that fix at ALT and SPD. You need a frequency. FSX/P3D can't do HF, so it'll be one frequency. (Otherwise you'll get a Primary and Secondary HF freq IRL.) The Initial call is important bc it has the most stuff. You'll get a hand off sometime before the fix. If you didn't get a freq, ask before you go.
Make Initial Contact. "Gander Radio, Gander Radio, XXXXX, On XXXX (Freq), Position." Add "SELCAL XX-XX, CPDLC" if you want.
They will come back asking for an Estimate for initial fix, FL, and Mach typically. Easy!!!
So as you cross that initial fix...below follows.
The you need to remember this. PTAPTP!!!. Position Time Altitude, Position Time, Position. "Delta 55 Crossed XXXXX at 1255Z FL, estimating XXXXX, XXXXX next." Atlantic adds the Mach after the FL, but they should know the Mach already since you requested it. EVERY FIX YOU CROSS REPORT! Make yourself a form and just right the info down. In some agreements with controlling agencies if your FMC time to a fix is great that 2 or 3 mins (pending where), call the controller and adjust it. Just do it.
This is sometimes a learn as you go thing. Important to know though...know where you are, report where you are, stay on course/on time. This is the basic stuff. Don't adjust ALT either unless requested.