How can I get the cup stains out of this table?👇seemore

Those white rings are usually moisture/heat trapped in the table’s finish (often lacquer or polyurethane), not damage to the wood itself. Start with the gentlest method first:

Clean the surface
Wipe with a damp microfiber cloth and a little dish soap.
Dry completely.
Use gentle heat (works surprisingly often)
Put a clean cotton T-shirt or towel over the marks.
Use a hair dryer on medium heat or an iron on low/no steam.
Keep it moving for 10–20 seconds at a time.
Check frequently. The white haze often disappears as the moisture leaves the finish.