Basically hold the front brake and pedal. Do it both standing and seated. It's the easiest way to isolate the seatpost and seatclamp as the culprit or not.
Then do the basics. Skewers, chainrings, headset, whatever. Bottom brackets are frequently the culprit on older bikes or bikes that spend a lot of time riding in wet conditions, but those are also the most work and expensive option, so save that for last
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