I bought an old house and found that the socket had no grounding wire and the direction of the wire was unclear. I don't know how to remedy it, to prevent electric shock.

In an old house, if the tap water pipes at home are all metal pipes and are reliably connected to the earth, you can find a wire, peel off the skin of the wire, tightly wind it around the metal tap water pipe, and then connect the wire to the grounding interface on the socket.

If the tap water pipe is not a metal pipe, or it is not connected with the earth, the simplest way is to buy and install a leakage switch to solve it.