As a participant
In order to be eligible you have to be female and be eligible to participate at IOI in the same year. For this, you havo to be not older than twenty years on July 1st and you have to be enrolled at a school not higher than secondary education. For details, please see the EGOI Regulations and IOI Regulations.
Responsible for selecting the delegations are the national organizations who run the national olympiad in informatics. Get in touch with your national organization to find out more about the local selection process. See here for contact information for most countries.
As a national olympiad in informatics
Currently, there is no fixed process to become a member of EGOI. You will probably receive an invitation from this year’s host with more details on how to register. If you do not receive an invitation, feel free to reach out to the host.