To improvise or play casually on a musical instrument, especially a guitar or piano. He spent the afternoon noodling on his guitar, coming up with new melodies.
To catch catfish by hand, typically by allowing the fish to bite one’s arm (U.S., chiefly Southern). They spent the afternoon noodling in the muddy riverbank.
To think about or ponder something in a casual way (usually followed by "over", "around", etc.). She noodled over the design until a better idea emerged.