Systematic guessing as a last resort
Trial and error involves making an assumption and following it to a conclusion.
Not a preferred technique, but sometimes necessary for extreme puzzles.
Choose a cell with few candidates (preferably 2).
Assume one value and follow logical consequences.
If you reach a contradiction, that value is wrong.
If no contradiction, you might need to guess again deeper.
Systematic approach: always backtrack properly.
Some call this "bifurcation" or "what-if analysis".
Purists avoid it, but it's a valid solving method.