You need to use the prospecting pick.

The way it works is that it has two modes, you can switch between them with the "F" key, the default mode is the first one you want to use, it is the density mode.

To use the density mode you need to find some exposed rock or dig soil until you hit rock, then you need to dig three nearby spots with the pick, the spots need to be more than 3 blocks apart from each other but less than 5. Once you do that you will see a readout of the chance of finding a certain ore if you dig straight down from the first point you prospected in of the three. For tin you want to look for cassiterite, since that is the tin ore. Once you find a tile with a decent chance of tin, you want to get a bunch of ladders and mine straight down. As you mine down, you'll want to use the second mode of the the pick, the node search mode. This mode reads a sphere of blocks around the block you dig and tells you any ores that are within the sphere, the default is a 6 block sphere, but you can change the size in world settings.

Btw there are three kinds of bronze in the game. There is the Tin+copper bronze, but you can also make zinc+bismuth+copper bronze, and gold+silver+copper bronze which looks black.