There are four major methods for making graphene. The fastest is probably micromechanical exfoliation which is just a fancy way of saying that you peel a piece of graphene off of a piece of graphite using a piece of scotch tape. This method results in sheets of single layer graphene, around 1 mm².

To make larger sheets of graphene, epitaxial growth with chemical vapor deposition (CVD) is used. In this method, a layer of graphene is grown on a metal surface by decomposing hydrocarbons. These layers are around 1 cm².

Another method for making "large" graphene sheets is epitaxial growth on a crystalline SiC substrate. The size of graphene sheets grown on SiC is determined by the size of the substrate, so they can be fairly large. The graphene sheets must be removed from these substrates by etching.

The final method is exfoliation of graphene in a solvent to create colloidal suspensions of graphene. However this method is not usually used to make single-crystalline graphene samples. Instead, the solution is deposited on a surface to make multi-crystalline graphene layers.

Graphene is not completely transparent to light, although a single layer has >99% transmission. Multiple layers of graphene will indeed absorb more light.

References:
Zhu, Y., Murali, S., Cai, W., Li, X., Suk, J. W., Potts, J. R. and Ruoff, R. S. (2010), Graphene and Graphene Oxide: Synthesis,Properties, and Applications. Adv. Mater., 22: 3906-3924. doi:10.1002/adma.201001068
Geim, A.K. (2009), Graphene: Status and Prospects. Science, 324:1530-1534. doi: 10.1126/science.1158877
Park, S. and Ruoff, R. (2009), Chemical Methods for the Production of Graphenes. Nature Nanotechnology, 4, 217-224.doi:10.1038/nnano.2009.58