To access the Access Policy:

• Click on the queue
• Go to the Access policy tab
• Click Edit

You will need to edit the policy in JSON. I think there was previously a simpler way to add permissions, but that method simply modified the policy. Now you need to edit the policy manually.

You can use the AWS Policy Generator to help construct a policy.

Looks like when first creating the queue in the new console, it has a wizard that lets you add other AWS accounts, IAM roles/users - but after the initial queue creation, if you go to edit the queue, that wizard isn't there.