Although I am only a student Pilot, I think this answer is good enough!
I'm going to use my home Matz and aircraft for an example
Me: 'Benson Zone GWACG request matz transit and flight information service'
ATC: 'GWACG Pass your message'
Me: GWACG is a Cessna 152 from Wycombe to Gloucester via oxford overhead. 1 mile south of Stokenchurch at 2000ft on QNH 1021, request MATZ transit and flight information service'
ATC: GCG squawk 3061 Matz transit approved 2000ft on Benson QFE 1011, flight information service
Me: Squawk 3061 MATZ transit approved at 2000ft on 1011, flight information service GCG
Later
Me: GCG is clear of the MATZ switching to Oxford Tower on 125.325
ATC: GCG squawk 7000 good bye
As I said this is only an example for crossing a MATZ, you can find a template for this inside your PPL RT book (which i assmue you have)
As for your airfield being located inside a MATZ i imagine you have a process unique to your airfield, probably to do with booking in with the RAF before you leave. But i recommend asking an instructor there before you leave.
Hope this has been of some help