1) The custom is to go to a river or well of water on the first day of Rosh Hashanah after the afternoon services, and there they say the rite of “Tashlich” which is in the prayer-books, and they empty the hems of their garments as a sign and allusion, to pay attention to throw away the sins, and to make sure that from now onwards they will be free from sin. There are many reasons given for this custom: 1) To remember the merit of the Akeidah, where the satan made himself appear like a river to try and obstruct Avraham and Yitzchak. 2) Since on this day we make Hashem rule over us and the place to anoint and appoint kings is on the bank of a river. 3) To remind us that we are compared to fish, who can be caught in a net at any time, and by reflecting on this we will think more about repenting. (Kitzur Shulchan Aruch 129)
2) After returning to the synagogue if it is not yet time got the evening services one should be careful not to sit with groups of friends, so that he will not, G-d forbid, come to idle chatter. Instead, he should occupy himself with Torah or Psalms or books of self-correction, for the day is holy for our Master. (ibid)
