We demonstrate that Dirac fermions can be created and manipulated in a two-dimensional electron gas (2DEG). Using a cryogenic scanning tunneling microscope, we arranged coronene molecules one by one on a Cu(111) surface to construct artificial graphene nanoribbons with perfect zigzag (ZGNRs) or arm-chairedges and confirmed that new states localized along the edges emerge only in the ZGNRs. We further made and studied several typical defects, such as single vacancies, Stone-Wales defects, and dislocation lines, and found that all these defects introduce localized states at or near the Dirac point in the quasiparticle spectra. Our results confirm that artificial systems built on a 2DEG provide rigorous experimental verifications for several long-sought theoretical predications of aperiodic graphene structures.