Find clay rather than a fixed direction
Tin is mainly found in sparkling Clay Blocks in the Clay Caves. Begin exploring toward that region during the copper stage.
The Clay Caves and Forgotten Ruins surround the starting underground area, with an orientation that varies by seed. If your route continually reaches grey stone walls and ruins, move around the inner region to look for clay. There is no universal instruction to dig left.
Mine and smelt
Mine the sparkling tin deposits, then put Tin Ore in a Furnace to make Tin Bars. Use the bars for the Tin Workbench and further tools in the crafting chain.
Mark a Tin Boulder for later. A Crude Drill can automate boulder mining, but it is not required for your first tin.
When tin is hard to find
Check the biome, wall appearance, tool and item name in your inventory. Exploring beside Ghorm’s track is one possible search suggestion, not a guarantee that every stretch contains tin.
The official 1.3 update increased tin in the Clay Caves. It did not promise a minimum amount in every world or establish that already explored parts of an older world receive fresh ore.
The useful success check is simple: Tin Ore in your inventory, then Tin Bars from the Furnace. Do not rely on an unsupported fixed radius or a guaranteed drop probability.