I can't find my association
Your association appears on your overview when your membership is connected to the account you are signed in with. If you do not see it, it is almost always an invitation that was never accepted — or you are signed in with a different address than the one the association invited.
Go through this
Check your overview for a pending invitation.
An invitation you have not answered shows as "You are invited to …" at the top — tap "Join".
Search your email for the invitation.
Check the spam folder too. Open the link in the invitation email and follow the steps.
Ask the association which email address they invited.
If it is a different address than the one you sign in with: sign in with that address — or better, link it to your account under Account → Email addresses, so the invitation finds the right place.
Signed in to the wrong account?
If you have ended up with two accounts — for example one created via an invitation to your work address — the association lives on the other account. Read the article "Two accounts? How to gather everything into one".
If you are not a member yet
Membly has no association search — you join via an invitation from the association or via the association's own public page, where you can tap "Apply for membership". Ask the association for an invitation or for the link to their page.