There are many ways to join an official series.
From the iRacing UI (aka desktop icon):
Click Racing...Official
Under that you can choose either Official Series or Up Next
In Up Next or Current Series, you can Filter to show what you want to see
and in the results, you can sort by any of the columns, for example, License Group
then click the green Register button for the race (or session) you want to get into
Follow the online instructions and then click Join when prompted:
