typically bare copper of the same guage/size as the wire feeding the outlet...usually either 14 or 12 gauge ...run into each outlet box in the wall. then these bare copper ground wires will then need to run back to a juntion box where a lrger gauge copper wire should be tied to like a cold water copper or galvainzed pipre in the attic or basement whichever case applies to you where eventually that water pipe runs out of the house into the earth...which Earth Ground. ...I did the bare copper wire addition to some of my old 2 wire outlet circuits in the front of the house (it was built in 1949).
the other option is to replace each out with a GFCI outlet---I believe this should work too...with out running extra wires anywhere.
Best thing really is to hire it out to an electrician...because you want it done correctly and safely. good luck LJ