Depending where in the Western US and depending on the culture and weather, the homes people were building could be quite different, and the answer to your questions could be quite different.

1 - for many places, people didn't actually use many "boards" in their houses. Lumber was a luxury in many places, so people made log houses. You've probably seen broadaxes around at flea markets or similar stores - those axes are basically a finishing tool for squaring logs or finishing the surfaces of split logs. Often logs would be squared, or at least have two sides squared, then the resulting house would be chinked, mudded and whitewashed resulting in a house that would look very much like a later stick frame house. Doors and floors, window frames, all could be either whipsawed or split on site, and splitting wasn't that complicated a process, an axe can help but you can make do with wooden wedges and hammers.

2 - one of the main industries in a lot of places was actually producing lumber! well before 1900 there were steampowered and water powered sawmills all over, especially along the coast of the pacific.

3 - I already mentioned it - but whipsawing. The standard way of producing lumber without a sawmill was using a whipsaw - put your log on a frame, one man above, one below in the pit, and you saw. If you were making boats to head to the gold rush or if you were constructing a building with lumber, having a whipsaw was a must, and there are places where this is still a thing.

And I guess that answers the question - between sawmilling (which was absolutely a thing), whipsawing and splitting boards out of logs with wedges and finishing them with hand tools, people had access to boards, both for purchase and also making them themselves.