noun
Refers to a way of doing something, often implying a skill or know-how. Commonly used in expressions like ～すべがない (there is no way to ...).
彼に連絡するすべがない。
There is no way to contact him.
生きるすべを身につける。
Acquire the means to live.
方法 is a more general and common word for 'method' or 'way'. すべ often carries a nuance of a practical skill or a last resort, and is frequently used in negative or desperate contexts.
手段 refers to a concrete means or measure to achieve an end. すべ is more abstract and often implies a learned ability or a way out of a difficult situation.
The origin is uncertain, but it is a native Japanese word. The kanji 術 is an assignment based on meaning, not etymology.