noun
Almost always used in negative patterns such as なすすべもない (have no means) or なすすべもなく (without any way). Describes a situation where one is at a loss and has no course of action.
See also: なすすべもない
突然の停電で、なすすべもなく暗闇に座っていた。
With the sudden blackout, I sat in the dark without any means to do anything.
彼はなすすべもなく、ただ相手の言いなりになっていた。
He had no way to act and simply did as the other person said.
手段 is a general, neutral word for 'means' or 'method' used in both positive and negative contexts. なす術 is limited to negative expressions of helplessness.
方法 is a broad term for 'method' or 'way' and can be used freely. なす術 is only used when emphasizing the lack of any method.
From 為す (なす, 'to do') + 術 (すべ, 'means, way'). The reading すべ for 術 is an older native Japanese word for 'method' or 'technique'.