You need to click on the 'tournaments' icon near the top of the page. New and 'in progress' tournaments are shown there, and when you click on one that isn't started, you will see where you can join.
There is no set schedule for when new tournaments are being established, so you just have to keep checking regularly.
Also, joining a tournament is open to all pawnstars, so it's not by invitation only. Some tournaments do have rating limits, so you may not be able to enter those because your rating doesn't meet the parameters.
The only one currently being started is limited to members with a rating of 1150 or less, so you probably can't join that one. You will see a few entrants who have a rating above the limit, but they probably signed on when their rating was lower, and have won some games since then causing their rating to increase above the limit.
hope that helps...