As stated by yoyomoer_xD, the ELO
tournament is a weekly event.
To participate, one simply must enter the ELO
room and have taken part in at least 5 matches.
Sunday marks the end of the ELO
tourney, as well as the start of the next one.
So, once you've meet the requirements, even if you haven't done much, at the end of the week, Kate will send you a pm stating you've taken place in the tournament, and you'll receive 150 clintz and 2 credits I believe.
Head to the ELO
game rules via the "The Game" drop down list, and you'll find the prizes given to players.