When and from which agency you request your NAT clerance depends on the route you fly and where you are located.
Flying via the Shanwick area westbound and departing well outside of this area, you will receive the "normal" ATC clerance while still on the ground, e.g. in Frankfurt form the respective clearance delivery position.
While airborn you will then contact Shanwick on VHF and ask for your clearance. In this call Shanwick needs the requested Mach No., FL, entry point and the ETA for this point.
After coordination is finished Shanwick will come back with the clearance giving you the Track (if you fly one) or the coordinates if on a random route, the Mach No. and FL. Flying a Track you have only to read back the Track, Mach No. and FL and the Track Massage Information No. stated on the relevant NAT Track Massege issued by ATC.
If you are following a random route which is defined by LAT/LON coordinates, you will also have to read back the exact coordinates as given in the clearance.
Nowadays with ACARS, the clearance is easily requested by ACARS (datalink), avoiding communication using VHF, which could be very busy. With this feature you have to fill in the same information on a mask of the ACARS screen, which will then send your clerance request to Shanwick for example.
The clearance itself is then sent to the aircraft also via ACARS.
Flying via Santa Maria or Rykjavik areas, you will use VHF to get your clearance even today.
Regarding position reports, you will have to call ATC on a given VHF or HF frequncy whne ever crossing a LAT/LON coordinate given in the Track Message or while on a random route the LAT/LON coordinate given in the clearance.
Contents of a position report is standard giving the coordinate, the time when passed this coordinate, FL, estimated time for the next coordinate or fixed waypoint and the next following coordinat or point . Following a random route you will also have to include the weather, mainly wind and temperature at the reporting position.
Hope this helps.