You can't assign users to a block...you assign roles/permissions, meaning anyone with a particular role has permission to do something with the block (usually view).
- Turn editing on (where ever the block is).
- Click the actions button (also known as Configure and Editing) on the block.
- Choose Assign roles in *** block. It will tell you that this is not possible.
- Go back to the Administration block and choose Permissions.
- You'll see a short list of permissions and you can add/remove roles to these permissions, as needed.
Since everyone is an authenticated user, it shows up for most blocks but with custom roles, you will probably have to add the role to the permissions. Hope this helps.