There are some great resources for finding your ancestors, and building your family tree.
There are websites that have transcripts for various historical records. These are generally reliable, and I recommend the Archives Office of Tasmania's Convict records, and the Tasmanian Colonial Family Database, as good starting points for Tasmanian History. Of course with these it is necessary to have a little bit of knowledge about what you're looking for.
I stress caution with websites where the information recorded is user-input. These can contain mistakes, and those mistakes can be copied many times over, into 'merged' accounts and perpetuate the incorrect information. It's really important to research some official records to back up your connections before you 'set them in stone'.
A great resource for Australian research is the National Library of Australia's newspaper transcripts - called TROVE - these have been digitised using optical character recognition - that's a type of scanning where the scanned data is turned into editable text. The OCR makes some interesting errors. Registering to be able to edit, and making changes to the digital format, gives others a more searchable resource. And it's fun.
Other do's and don'ts:
Be flexible about spelling - before the 20th century it wasn't as important as it is now. If you're searching for Stephens, be prepared to include Stevens, Stevenson, Stevins, etc. Usually names were written down according to pronunciation and the best guess of the person writing them. It would also be dependent on who reported the event to the registration body at the time.
Be careful listing living people on public websites - there are privacy issues, and some people may not want their personal information listed where others can access it.
Be equally cautious contacting people - we now have access to online telephone directories and it's possible to find people's phone numbers or addresses - this does not give you the right to contact a person you do not know. They may not appreciate your enquiry. They may not be interested in the family history, there may be a background of family conflict that you are not aware of, or some other reason why they don't wish to be involved.
Check your sources - especially with sites like Ancestry.com - which is a wonderful resource for documents and records, but also has a user generated aspect which may, or may not be accurate. Find collaborating evidence, if possible, before you put something in place in your tree.
Be willing to be shown to be wrong - maybe the person who found the information, and passed it on to you, was 'barking up the wrong tree' :) This happened with my husband's family tree, that was published in a lovely magazine style book, but the person who did the research linked the wrong family to the arrivals in Australia, and got it all wrong from there back.