His chief goal was to convert King Æthelbert of Kent. The illustration shows Kent to be a fairly small area, but Æthelbert was powerful as a bretwalda and was respected and listened to by neighboring kingdoms. He was also married to a Frankish princess, Bertha. This link to the continental kingdom not only helped his influence, it made him open to Christianity, since Bertha was a practicing Christian.
Æthelbert allowed the missionaries to preach and use a church dedicated to St. Martin as a base. Æthelbert did convert, and was probably baptized at Canterbury. We don't know when he converted, but letters dated 601 from Gregory refer to him as "my son" and mention his conversion.
With the king's conversion, a community-wide conversion became possible. Augustine mentions making lots of conversions within a year of his arrival. In 598 Augustine wrote to the patriarch of Alexandria claiming he had baptized more than 10,000.
With many conversions progressing, Augustine sent one of his companions, Laurence, back to Rome with questions for Gregory about organizing the church in Britain: who could marry whom, how to deal with church robbers, consecration of bishops, relations between the churches of Britain and Gaul, etc. Messengers from Rome eventually brought a pallium from Gregory to Augustine, making him a bishop.
One bit of advice was to shift feast days of the locals to days celebration Christian martyrs, and to turn religious sites to shrines for saints.
Obviously the Gregorian Mission worked, and Augustine became the first Archbishop of Canterbury for his efforts. There is someone else who should get more credit for Britain's conversion, however, and that is Bertha. I'll tell you more about her next time.