First thing you will need is a port of entry.
To find it, you need to step back a moment. Where did the person come from? This information would give you a list of the most likely exit ports from their home country and entry ports in this country. From that, you will be able to develop a list of the shipping lines serving those ports. And, you can also develop a list of names of vessels plying those routes.
The next thing is to work your way through the passenger lists. Check to see if the ports of entry have Maritime Museums (as Liverpool has)
http://www.liverpoolmuseums.org.uk/maritime/
Check to see if they have their own website by doing a search on \"Maritime Museum\" and the name of the port.
Some useful information can be drawn from these websites and, you may even be able to get the information you are looking for almost immediately (I hope so).
Keep us advised on what you have done and what, if anything, you have found. If necessary, we\'ll try and help further.
Good luck
Keith.
Australian immigration records 1880s