These competitions don't need a precise answer. Your answer just allows them to have the wine judged along with other similar wines and not a jarringly sweet wine in the middle of a dry wine flight.
You can estimate the RS by hydrometer (dry is roughly 0.990 and every additional 0.010 reading is about 2% RS), by refractometer ( dry wine reads about 5.5 on the brix scale so each additional brix reading is about 1% RS), or if you added sugar you can figure the grams per liter added (10g/L is 1%). I'm sure others can suggest other methods too.
There is another method that uses clinitest tablets to measure the reducing sugar (urinalysis tests) but it can't measure any sucrose you've added since that isn't a reducing sugar.