Removing a stamp from an envelope is the first step towards a coveted place in the stamp album. Never try your luck to peel a stamp adhered to the paper. It always tear or thin off before you can apply the brakes!
Standard procedure: select a sufficiently large container and fill it up with luke warm water. Soak the cut out pieces for 10 to 15 minutes. This generally works for most stamps with normal glue. Never leave the stamps for extended period - this softens the stamp paper fibres excessively and renders the stamps vulnerable to damage during handling.