How do mining companies find mineral deposits?
Primarily through prospecting and exploration.
In the past centuries, many mineral deposits were located by amateur prospectors going into the bush and basically looking around! If they found a promising deposit, they would officially stake it with the government and then try and interest a mining company in buying it.
Today, while there is still some prospecting going on, exploration is usually done by professional geologists and geophysicists using sophisticated tools and computer models to find deposits. Fieldwork is still involved and interesting prospects are usually drilled to determine their grade of ore and tonnages. Most deposits, however, do not turn into mines - only the most economically attractive make it all the way to an actual mine. Junior exploration companies often complement large corporate exploration companies. If a "Jr" finds an attractive deposit, they might do some drilling, work it up a bit and then try and sell it to a major mining company.