June 11th is the anniversary date, but you can find celebratory events every day in June by going through the Neo Steam calendar. Click on events that look interesting to find more information as well as specific locations and times -- some promise more details to come, but there is plenty to do in the meantime. If you haven't tried Neo Steam and are interested in giving it a look, be sure to check out the daily beginner hour that is part of the celebration. The GMs will be appearing at different spots each day to help new players.
In-game events aren't the only part of the celebration. Each day you log in during June will earn you a brass gear that serves as a raffle ticket for a Neo Steam-themed iPad. During the month of July, Atlus Online will draw from those raffle gears and ship the iPad to one lucky winner.
The event is going on now, so check it out and have fun!