Peel off as much of the newspaper as you can, using your fingers.
Wet a piece of cloth in linseed oil. Rub the oil over the newspaper, saturating it in the oil, while taking care to get as little of the oil on the rest of the table as possible. You’ll want the newspaper to turn slightly transparent form the amount of oil that you apply.
Allow the linseed oil to soak through the newspaper, weakening its bond with the wood table beneath; 15 minutes should be sufficient time.
Peel off the wet newspaper by hand. Take care not to scratch any finish on the table with your fingertips. The newspaper should peel right off. If it doesn’t, dampen the cloth in the linseed oil again and use the damp cloth to rub the newspaper off of the table top.
Wipe away any traces of the oil after the paper is gone with a soft, clean, lint-free cloth.