There are 2 options to enter the GES or GEA: join an existing team or enter your own team.
In both cases, you need to apply for a GEM License first. Go to the GEM Licenses page and follow the instructions there to apply for a license. You need to pass the regulations test with at least 9 out of 12 questions answered correctly and then you need to choose which license you wish to apply for and submit your simracing resumé. The management will review your application and assign a license, usually within 1-3 days.
If you wish to join an existing team, you can go to the Drivers Market on the forum and post an ad about yourself there. Teams may not be interested in “hiring” you though, depending on whether they need drivers and what license and/or experience level they require. That is completely up to them.
If you wish to enter your own team when signups are open, you need at least 3 (GEA) or 4 (GES) drivers who all have their licenses. Then you can go to the signup page and fill out the form to register your team. You will need to pay the entry fee during the signup process. Please check the regulations for the license requirements per class, because your application will be rejected if it doesn’t meet those requirements. You will get an email informing you whether your application is accepted or denied. When your entry is accepted, you will get access to the restricted section of the forum, where you can find all the information you need. Make sure your livery is up to the required standards (regulations) and submitted before the next deadline.