Q:

Access an S3 bucket created by another user

Here's my scenario: I'm user Marius, and all I want to do is to:

access an S3 bucket created by user Admin,
upload some images there, 
access them, via CloudFront, later on.

Here's a summary of my attempts so far:

User Admin, using the AWS Management Console (AWS MC), grants List, Update/Delete, View Permissions permissions for his already created S3 bucket to User Marius.
To grant permissions we used this approach, using for grantee first the users email; then the AWS canonical userid, both of them falling back to the username.
User Marius uses CyberDuck to successfully connect to S3, using Access Key ID / Secret Access Key, but the root folder is empty. Accessing S3 through AWS MC doesn't help either:

To get started using Amazon S3, create a bucket to hold your objects.

The attempt to create a new bucket with the same name -- as per Tom Andersen's comment below -- fails: the bucket already exists.

What do I have to do to access that S3 bucket and modify it's contents?

A:

A secret and key only gets you access, you still need to create a bucket, which is basically like creating a new drive letter in windows, adding a new hard drive, etc. 
But you sound like someone has given you access. You may have two AWS accounts - one that has no buckets and one that you have been granted access to that has buckets?
Or the people who gave you access want you to make the buckets? If you know the bucket name, trying to make one with the same name will fail if anyone else on earth has already made a bucket by that name.

