In my case, I was lucky enough to connect with a distant relative who had done a lot of the research, and then confirm parts of it (I was at uni at the time - love a large library and databases!).

Her being a convict helped with the record keeping, of course - court records, ship records, habitation records on the ground. And even by the time she was freed, these were all tiny colonies* so recording everyone was pretty easy.

*How tiny? Well they evacuated the ENTIRE colony of Norfolk Island in about 1807, shipping them all to Hobart which was in need of a larger population. Even then, her daughter (my 7x great grandmother) was something like the 143rd wedding in the colony (now state of Tasmania). Compare that the USA circa 1807 which had 17 states in the union and a population of about 6 million.

The First Fleeters have been well researched and documented, as these people became the founding fathers (to borrow a phrase) of Australia.

I'm descended from this fellow:

http://www.fellowshipfirstfleeters.org.au/john-herbert.htm

who similarly spent time on Norfolk Island and then Tasmania. I expect his path probably crossed with the above great great [...] grandmother at some point.

The transcript of the court trial that sent him to Australia is available online. It looks like the whole trial lasted about 90 seconds. Reading the transcript, I learned that one of my commutes in London had me walking over the spot where he was arrested twice a day.

Australian governments, from the first fleet until today, have kept records of births, deaths and marriages.

For Australian history from 1788 onwards, The Fatal Shore by Robert Hughes is an excellent read. It also gives a good insight to British attitudes to criminality, of which traces can still be seen today in government policy, etc.