Repairing a simple bullet hole through fabric was a straight forward exercise that every rigger would learn in his training.
Essentially:
1) clean up edges of the hole ensuring there are no tears or runs. Inspect to ensure there is no internal damage. Lightly sand around the edges of the hole to open the plies of the fabric.
2) prepare a fabric patch at least 1″ wider all round than the damage.
3) Tease out the edges of the patch so that they appear frayed. Modern repairs use pinking shears which make a saw toothed edge.
4) Apply dope around the damage cut out (over the sanded area), apply patch and dope over the patch.
5) When dry the dope will have tautened the fabric. A second coat is sometimes required.
6) Apply coloured dope as required.
Larger patches require the fabric to be sewn as well as doped.