We drove in from North East London for a 10 am appointment - didn't fancy exposing the babies to rush hour on the tube!!
There is a huge underground car park at nearby Hyde Park Corner, which will keep you out of the congestion zone. Access is off Park Lane (northbound). It's a pleasant walk from there to the Embassy. We parked there.
Otherwise, if you drive into the congestion zone, it's not such a big deal - all you (or your Dad) have to do is buy a £5 ticket by midnight that day (by phone, online or at a newsagent) and that's it. Easy! There's on street meter parking around the Embassy.
Chris