"All critical thinking begins with understanding meanings." What four things do you clarify about a statement?

What is claimed, the concepts used, the intention behind it, and the context it was said in.

A truth-claim can't even be raised — let alone made good — if its terms are unclear, so meaning-clarification comes first. Four facets:

1. What is being claimed? Strip away abstraction, metaphorical ambiguity, political loadedness. Make sure both sides are "talking about the same thing"; dissolve metaphor into precise conceptual statements.
2. Conceptual clarification. Find examples and counter-examples; point at the objects the term covers; in a scientific context, give explicit definitions that normalise usage.
3. Intention. Speaking is also acting — asserting a fact (which can be true or false) is a different speech-act from warning, praising, requesting or provoking. The same words can mean very different things depending on the intended act.
4. Context. Meaning depends on socially established usage and on the situation an utterance was made in; the same sentence shifts meaning across contexts.

Tip: Intention and context are the easy ones to forget. A literally identical sentence can be a sober factual claim in one mouth and a provocation in another — and only one of those is "true or false."