One week in real life is one month in Lathe. There is chronological flexibility as to when events actually occur, so you could start a scene with an another player on Monday and finish it Wednesday while still saying it happened in the first week of the month. Stories are based on major events in the city, with the estimate of around one real life calendar month per story.
Playing once per week grants you 5 Experience, playing twice per week grants you 5 Experience each time for 10 Experience total. Playing more often than that is encouraged, but yields no further standard Experience rewards. Up to 10 Solar Experience can be gained per week from hitting various goals such as exploring intimacies, organizing player-run events, driving the story forward and so on.
Solar experience can be gained from the following categories, each category maximum once per week.
Expression (2) - Showcase what the character is. Standard fare from the core book.
Role (2) - Display your caste's function or spotlight others. From the core book. This also includes doing something that fits your major or defining ties, goals or character concept or spotlighting someone else's goals/concept.
Event (2) - Run an event or scene in which other players participate or showcase an aspect of the game setting. This can be as small as "I want to meet up with you in the Haunches" or "My character is performing at the Birdcage today". Players are also allowed to run events or small plots with ST permission using distinct NPCs, though this needs to be negotiated.
Connections (2) - Change of intimacies (creating, weakening, strengthening), especially between player characters. This means you will be rewarded for befriending or opposing other players.
Misc (2) - Help players out in chat, vote for their stunts, do non-game related stuff like help out with the wiki, kiss up to STs.
Stunts are always 1 points unless voted on by other players to be higher. Other players can vote in the OOC chat simply by saying "+2" or "+3" and mentioning the player about to perform the action. Needs at least one player for the +2, generally max twice per scene. Needs at least two other players for the +3, generally max once per day. Just because your character is at odds with an another, doesn't mean you shouldn't vote when you think their stunts are cool. Be a good sport and you can earn your Misc experience easier.