Eating and drinking after concluding the meal:
Verbalize that one is not accepting the fast at the meals conclusion: One may eat and drink after the meal until sunset. This applies even if he decided in his mind to no longer eat or drink after the meal. Nevertheless, it is best for one verbalize prior to ending the meal that he does not plan to begin the fast until sunset.
If one verbally accepted the fast: If one verbally said he would begin his fast after the conclusion of the meal then he may no longer eat or drink after the meals conclusion, as these words have the status of a vow. If the person decided that he is accepting Yom Kippur after the meal, then if he verbalized this past Plag Hamincha he must begin to keep all the laws of Yom Kippur from after the meal.