Water near the tank can come from piping, valves, a drain, a pan, condensate, or the tank body.
The short answer
Keep away from wet electrical parts and do not operate gas, power, or pressurized controls without the appropriate knowledge. Record the first visible water point and whether flow is active. If a known safe water shutoff is needed, tell the provider exactly what was closed.
What to notice
Look from top to bottom
Without removing panels, note moisture at upper connections, along the body, near a relief discharge path, at the drain valve, in the pan, or from nearby equipment. Water can run down the tank before reaching the floor. A dry fitting above a puddle does not eliminate an intermittent source.
Preserve temperature and equipment clues
Record equipment type, model, approximate installation information if documented, water temperature changes, sound, error displays, and recent service. Do not cap a relief line or change controls to stop water. A safety device discharge needs its cause evaluated, not merely redirected.
Compare the full replacement boundary
If replacement is proposed, ask about capacity or performance, fit, venting or electrical needs, shutoffs, drain pan, discharge routing, removal, permit, inspection, and warranty. Floor or wall damage and drying may be separate. Ask what makes repair inappropriate rather than accepting age alone as the explanation.
One useful question
Can I keep using a leaking water heater?
That decision depends on the leak source, equipment, and surrounding hazards. Do not keep testing equipment that is releasing water or affecting power or fuel systems. Stop use and obtain prompt qualified guidance, explaining the current water and energy status.