This invention provides an innovative method to manufacture graphene layers or quantities and graphene oxide layers or quantities from graphite, coal slags, asphalt, and other carbon-rich sold materials in nature. The present invention uses controllable microwave irradiation to heat the mixtures of basic material, graphite, or coal slags, or asphalt, or their combinations with ionic liquids and surfactant plus environmentally friendly oxidation agents. This invention can generate the said-products of graphene layers and graphene oxides in a short time period of one second to 300 seconds. The present invention does not involve any concentrated sulfuric acid, nitric acid, nor huge water quantities needed for the purification, unlike the prior art. The as-produced graphene-based materials can be used for preparing conductive films for touch screens, producing graphene carbon fibers and three-dimensional porous graphene nanomaterials, and preparing graphene-based other intelligent nanocomposites for super-light-weight machines and vehicles.