If graphene is a promising material in many respects, its remarkable properties may be impaired by unavoidable defects. Chemical vapor deposition-grown graphene samples are polycrystalline in nature, with many grain boundaries. Those extended defects influence the global electronic structure and the transport properties of graphene in a way that remains to be clarified. As a step forward in this direction, we have undertaken quantum mechanical calculations of electron wave-packet dynamics in a multigrain self-supported graphene layer. Our computer simulations show that a grain boundary may act as a reflector at some energies and for some incidences of the Bloch waves. In addition, our calculations reveal that when two grain boundaries run parallel to each other, the graphene ribbon confined between them may behave like a channel for the charge carriers. We emphasize therefore the possibility of creating nanoscale electronic waveguides and nanowires on the graphene surface by a controlled engineering of its grain boundaries.