Method for obtaining solid samples or suspensions of graphene optionally doped with heteroatoms from synthetic or natural polymers, which are subjected to pyrolysis in a furnace without oxygen at temperatures of between 400°C and 1,200°C and subsequently to a liquid-phase exfoliation phase. The polymers used are preferably polysaccharides, such as chitosan, alginate and alginic acid, which can be optionally doped with any heteroatom. The invention is intended primarily for use in microelectronics and photovoltaic devices in which graphene sheets are very useful. In addition, the graphene prepared cn be uses as an additive for polymers and ceramic materials.