The antenna mast needs to be grounded to the same ground system that the building's electrical service uses.
Normally, there is at least one ground rod driven into the ground close to the service entrance (where the electric meter is located).
You would run your ground conductor to that point, attaching it to the existing ground conductor, or directly to the ground rod using the appropriate clamp.
In the U.S. you must use #10AWG wire or larger. The lower the number (#8 is larger wire than #10), the larger the wire.
For my new Ringo Ranger installation, I have #4 wire.
The true point of any antenna ground system is to discharge the atmosphere in the area of the antenna, which should actually reduce the chance that the antenna or any part of the house being hit by lightning.
As for the radio itself;
It must also be properly grounded. You should also use a lightning arrester in the coax line between the antenna and the radio.
I am just going to disconnect my radio from the coax when it is not in use, and will never use it during a lightning storm.
One more thing;
There should be an instruction sheet included with your antenna which clearly describes the grounding procedure. Including this sheet and the warning labels is law in the U.S.
But if you either bought a used antenna, or are re-installing one, I wouldn't be surprised that you don't have the instruction sheet.
Hope this helps
FW