There are three large exchanges every year: Secret Santa in December, Arbitrary Day in June, and Halloween in October. You can see when these exchanges will take place on the calendar that is linked on the sidebar of the subreddit.
There are also tons of other fun, interest specific exchanges throughout the year. If you mark your profile and make sure the box beside “Receive upcoming exchange notifications?” is checked, you will get an email when they are announced.
Please note that matching happens at different times of the sign up close date for each exchange. This generally happens between 8 a.m. and noon PST, so be sure to sign up and link your account and validate your email address before the close of sign ups.