You stop at the R and change if to a Z. Barry = Baz, Darren = Daz, Carol = Caz etc etc. Because British English is non rhotic, it doesn't work if we stop at the R (like USAians can say "Gar" for Gary) so the z sound gets used instead, because it's pretty close.
Then the A gets added if you're being extra friendly or cute, a bit like Michael > Mike > Mikey. Gareth becomes Gary becomes Gaz becomes Gazza.
Make sense?