On a bowler's Leagues tab, under own leagues, tap Add a league: the name, the center from the directory (or the place typed in when it is not listed), the night and start time, the season, games per night, and the house handicap rule such as 90% of 220.
When you log a session, pick the league under League night; it is preselected when the date matches the league's night. Every tagged night feeds the average, high game and series, handicap, and the night-by-night list on the card.
These records are private to the bowler. They are never listed or suggested to anyone else, because nothing verifies them. If the league's secretary later runs it on Pinlocity, you join the roster the usual way and both show side by side.