This somewhat of a naive question.
Firstly what type of ore do you want: iron ore, gold, tin, nickel, copper, silver-lead-zinc, lithium, ... etc. Also, the difference between an ore deposit and a mineral deposit is economics - can profit be made by digging it up, processing it and turning it into a saleable commodity: gold bars, ingot or sheets of copper, concentrate of certain metal sulphides.
The other thing is, if you found something, what are you going to do with it. Within Australia there are laws and regulations regarding what can and can't be done regarding mineral resources. This is partly due to the State wanting it's cut via royalties and so the environment is supposedly looked after and neighbors are not affected - people living in towns etc. The State doesn't want to waste money cleaning up someone's environmental damage!
The other thing is, mineral deposits occur in certain types of geological settings. It's unlikely you'll find gold or iron ore in Sydney, but you will find coal. Geological knowledge is critical to be able to find most mineral deposits. Additionally, most surface deposits have either been mined or deemed uneconomic. To find something valuable it will most likely be covered by a thickness of rock or regolith.
The other thing is, if you happen to stumble on something, it might be pegged by an exploration or mining company. Removing anything from such leases is an unlawful act and if you are found you could face legal action. However, you may have limited rights to explore for some things provided you have a Prospector's Permit for the state or territory where you want to search.
All minerals in Australia are owned by the Crown (effectively the State or Territory), you can't go grabbing stuff just because you want to. If you own property in Australia, you only have rights to the top 100 metres. A mining company can legally mine under you house if the mine is greater than 100 metres in depth and the company has the necessary leases, permits and authorities from the State or Territory government authorities.