The best way would be to run a new wire (GREEN) into the wall and through the box to the outlet.The other end of the wire should be connected to the ground in the circuit box( if it's fuses you need to update them). You could also connect it to your cold water pipe as it passes into the house( before the shutoff). Or pass it through the wall and connect it to your grounding rod or loop.
The only method that meets the national electric code (NEC) is to use a GFCI outlet. You are not required to attach a ground wire to a GFCI, although in the package is a label that should be place on the outlet cover. It states that there is no equipment ground. The GFCI will still "monitor" the status of the ground pronged appliance and react accordingly.
Self grounding outlets will fake a grounded state, but the grounds connecting the boxes does not satisfy the code based on ampacity of conductors
Using a ground wire to the back of the box also fakes a grounded state but does not meet the NEC
Self grounding outlets will fake a grounded state, but the grounds connecting the boxes does not satisfy the code based on ampacity of conductors
Using a ground wire to the back of the box also fakes a grounded state but does not meet the NEC