This depends on who and what you are. 

I'm an individual

OpenAthens is a tool used for institutional access - for example where an organisations such as universities, corporations, hospitals and the like have site licences for content such as journals and databases, they use OpenAthens as the way to tell those resources that the user who wants access is a member of that organisation and should be allowed in under the organisation's licence. 

If you are a member of an organisation that uses OpenAthens you should contact the library or equivalent part of that organisation. A good way to check this is to use the contact your organisation function on the password reset page: https://login.openathens.net/auth#forgottenpassword

If you are not a member of a participating organisation, you cannot get an account directly and will need to use other means to access the content you are interested in. The publisher will usually have a way for you to exchange money for access. 

If you are part of an organisation you think would benefit from OpenAthens though, you could tell them about us.

I'm a librarian, information manager, IT department or similar

You've taken your first step into a larger world. 

You are welcome to check out these documentation pages for a flavour of how you would administer an OpenAthens domain, but the best place to start to find out more will be https://www.openathens.net/librarians/