This procedure won't be much different than restoring in a typical domain environment, but there are a couple precautions to take. The first step is to make sure your backup is built on a single file source or you will see the following error when you attempt to restore. “The media set has 2 media families, but only 1 are provided. All members must be provided.” This has been caused by using multiple destination files during the backup procedure. Simply create a new backup using one backup destination source on the Destination setting. If you highlight just one file in this window the backup will still use both sources so make sure you clear any other destination files.
Secondly, after your backup is created compress the file before using your S3 browser to upload. This will save you a lot of time and space in your S3 Bucket.
After uploading the file to your instance use the SQL Mgmt Studio to restore the backup as if it were on a physical server. Once the restore is complete run the fix sysdba script and you're ready to connect.