The Beracha of "Ha’mosi" recited over bread covers all beverages that one drinks during the meal, with the exception of wine. And thus when one drinks during a meal that includes bread, he does not recite "She’hakol" over the beverage, as the beverage is covered by the Beracha of "Ha’mosi" recited at the beginning of the meal. This applies to all beverages, as mentioned, the only exception being wine.
However, a question arises in the common case of one who drinks tea or coffee after the meal, before Birkat Ha’mazon. (It goes without saying that once a person recites Birkat Ha’mazon, he must recite new Berachot over anything he eats or drinks subsequently.) Tea or coffee drunk after one has finished eating cannot really be said to be part of the meal, and it is thus questionable whether the Beracha of "Ha’mosi" covers these beverages in such a case. Due to this question, the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933), in his discussion of this subject (174:39), writes that one should avoid the problem by first reciting "She’hakol" on a dessert food, such as a candy, which is certainly not included in the Beracha of "Ha’mosi." When reciting the "She’hakol," he should have in mind to cover the tea or coffee, and this way he certainly does not have to recite a Beracha over the beverage. Another solution is to first recite Birkat Ha’mazon before drinking the tea of coffee, and then recite the Beracha of "She’hakol" before drinking. This is the ruling of several other authorities, as well, including the Kaf Ha’haim (174:40) and the Nehar Misrayim. This is also the position taken by Hacham Ovadia Yosef in his Yabia Omer (vol. 5, 17:2).
This Halacha is discussed in Yalkut Yosef – Berachot (vol. 2, p. 40; listen to audio recording for precise citation), which adds that if one does drink tea or coffee after a meal before reciting Birkat Ha’mazon, and he does not first recite a Beracha over a dessert, then he does not recite a Beracha over the beverage. In such a case, we follow the standard rule of "Safek Berachot Le’hakel," that we do not recite a Beracha in a situation of uncertainty.
It must be mentioned that this discussion does not apply to the nighttime and morning Shabbat and Yom Tob meals, which begin with the recitation of Kiddush. The Beracha over wine recited with Kiddush covers all beverages drunk henceforth, until Birkat Ha’mazon, irrespective of whether the beverages can be formally considered part of the meal. Therefore, if one drinks tea or coffee after Friday night dinner or Shabbat lunch, he certainly does not recite a Beracha and does not have to follow the suggestions mentioned above.
Summary: If one drinks tea coffee after a meal, he should preferably first recite Birkat Ha’mazon, as otherwise it is questionable whether he needs to recite a Beracha over the beverage. Alternatively, he can recite "Shehakol" over a candy and have in mind for the Beracha to cover the drink. If he does not follow either option, then he does not recite a Beracha over the beverage. This does not apply on Shabbat or Yom Tob when one recited Kiddush at the beginning of the meal, as the Beracha over the wine in Kiddush covers all beverages drunk subsequently.