On a communal fast, the leader says "Anenu" between the blessings for redemption and healing and finishes with "Blessed are You, God, who answers His people Israel at a time of troubles." (If he forgot, see above at the end of 119:4). We read "Moses sought the favor..." [Exodus 32:11] in the morning and afternoon prayers, whether it falls on Monday or Thursday or any other day. Rem"a: In the afternoon, we add the haftarah of "Seek out" ([Isaiah 55]) and in the morning there is no haftarah, except for on Tisha B'av. We read [in the afternoon] even if the fast is on Friday (Mahari"l). When fasting on Rosh Chodesh, we read the Rosh Chodesh reading in the morning and the fast day reading in the afternoon (Ra"n at the end of Chapter 1 of Ta'anit and Beit Yosef in the name of the Rokeach).
When the community declares a fast for some problem that they encounter, for the Monday-Thursday-Monday fasts after Passover and Sukkot that are done communally in Ashkenazi places, the early authorities have the practice that the leader says Anenu between the blessings for redemption and healing and they read "Moses sought the favor..." Rem"a: However, if a fast was set for Monday and Thursday, this does not supersede the regular reading of the parsha in the morning. Rather, in the mornig they read the normal parsha and in the afternoon, they read "Moses sought the favor..." The exception is the Monday-Thursday-Monday fasts that happen after Passover and Sukkot, on which we read "Moses sought the favor" in the morning and the evening. Such is the practice. [End of Rem"a] There are those who expressed dismay at this practice and challenged it. the Ros"h answered the change. Therefore, we follow the early authorities. However, in places where they declare a fast for no reason just in order to cause repentance, there are those who treat it like a communal fast with respect to Anenu between redemption and healing and the Torah reading and there are those who treat it like an individual fast, where even the leader only says Anenu during the "Listen to our prayers" section, and no Torah is read.
The leader only says "Anenu" as its only blessing if there are ten fasters in the synagogue. Even if there are ten fasters in the city, if there are not ten in the synagogue, he does not say it.
Some add penitential prayers in the blessing of "Forgive us," and there are those who do not say penitential prayers until the end of the Amidah. This is the practice of the early authorities in Israel, and it is the right practice.
On a communal fast, a prayer leader who is not fasting should not lead.
There are those who say that somebody not fasting should not read from the Torah and if the priest is not fasting, he should leave the synagogue and a non-priest who is fasting should read from the Torah.
On a public fast, two people should flank the leader, one on each side, and say penitential prayers with him.
All public fasts have priestly blessings at the afternoon prayer, except for Yom Kippur. Rem"a: In these parts, we only have the practice of doing the priestly blessings during the Musaf prayer of holidays, and this has already been explained in the laws of priestly blessings (Mordechai on Taanit and Hagahot Maimoni chapter 1).