Taanis, Chapter 2, Mishnah 2. In the previous Mishnah we learned that before the last seven fasts, prior to beginning the prayers, they would appoint someone to deliver words of mussar and rebuke before the congregation. Now the Mishnah continues and says: "Amdu bitfillah" - the congregation rises for prayer.
"Moridin lifnei hateivah zakein veragil":
"Moridin lifnei hateivah" - they bring down before the Ark.
"Zakein" - an elderly man.
"Veragil" - one who is very experienced and fluent in the prayers, and knows how to pray.
"Veyeish lo banim" - he has a household that depends on him.
"Uveiso reikam" - his house is empty and he has no food at all, and he himself is in genuine distress.
Others in the Gemara explain "uveiso reikam" differently: it does not mean that he has no food, but rather that his house is empty of transgressions and sins.
And why is precisely such a person chosen? "Kedei sheyehei libo shaleim batfillah" - these qualities enable him to pray with a whole heart, to concentrate and focus, without any distracting thoughts.
"Ve'omeir lifneihem esrim ve'arba berachos":
The eighteen of every day - the berachos we recite daily. In practice we say nineteen berachos today, but in the time of the Mishnah there were eighteen.
"Umosif aleihen od sheish" - six additional berachos, which were instituted especially for these fasts and for the last seven fasts.
In summary: In this Mishnah we learned the order of prayer on the fast days: they bring down before the Ark a chazzan who is elderly and experienced, who has children and whose house is empty - whether in the plain sense or according to the Gemara's interpretation that his house is empty of transgressions - all so that his heart should be whole in prayer. This chazzan recites twenty-four berachos: the eighteen of every day, plus six berachos that are unique to the fasts.