When people talk about an Oracle backup, they almost always mean a physical backup-- a physical copy of your data files, your control files, redo logs, etc. It's probably easiest to use Recovery Manager (renamed RMAN in recent versions) to do this if you've never done a user-managed backup before. If you take a physical backup, however, you can only restore it to a machine running the exact version of Oracle from the backup (and a similar operating system). Given how difficult it would be to find 8.1.7 installation media let alone a machine running a supported operating system, that may not be the best approach here.
You can also take a logical backup using the export utility. This generates a single binary file that has the DDL and data for either the entire database or for whatever schema(s) you actually want to preserve. This binary dump file can be imported into later Oracle versions but it will not contain information about things like the database configuration and it would not be possible to roll forward from a backup if later changes are made (thought that doesn't sound like a concern in this case).