What should I do when a GFCI near a sink keeps tripping?

A GFCI receptacle near a sink can trip for more than one reason, and I don’t want to assume the plumbing is involved or keep resetting it without knowing what’s going on. What safe observations can help narrow down whether the trips happen only with a particular appliance, even when nothing is plugged in, or alongside visible moisture or damage?

If it trips repeatedly, or the receptacle or surrounding area looks wet or damaged, should I leave it alone and have an electrician assess it? What should a qualified electrician check to confirm the GFCI is providing appropriate protection for that location, without me opening the receptacle or other electrical equipment?