I have a table "users" and I want to enable my visitors to login with their openID Account. For this I use the OpenId Component for Cakephp and it works fine (When I login with the Google URL I receive the "successfully authenticated!" notification).
But now I'm kind of stuck because I don't know how to go on from there.
No, you don't have to access the "oid_associations" table, it is a table which is only used by the OpenID library.
Instead, you can use the identity_url to figure out whether it is a new user. If that's the case, you can then create an entry in your "users" table. For example (assuming your "users" table has an "openid" column): 
$response = $this->Openid->getResponse($returnTo);
if ($response->status == Auth_OpenID_SUCCESS) {
    $user = $this->User->findByOpenid($response->identity_url);
    if ($user) {
        // existing user
    } else {
        // new user -> create user entry in the database
    }
}
I'm not sure I understand your second question correctly. If someone logs in with an OpenID and you get an Auth_OpenID_SUCESS response, then this means this user was sucessfully authenticated. How you use this information in your application is up to you.
I hope this answers your questions.
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