I want to upgrade my database from Oracle 8.1.6 to 9.2. I planned to get a full export to my old database and drop the database and then create the new 9.2 database and import the dump file into it. Is this the right method or not? If this way is right, what are some considerations I should take care of?
Using the export and import utilities to upgrade your database is definitely one of the "approved" migration methods. Your migration time for this method will be directly proportional to the size of your database. For those with larger databases, this migration method is not acceptable. Oracle's Database Upgrade Assistant (DBUA) uses a faster method, which many DBAs prefer. The DBUA migration method is not impacted by the database size. However, I do prefer the export/import method when I want to make some changes. For instance, you may want to start using Locally Managed Tablespaces, or the Oracle 9i new feature Automatic Storage Segment Management (ASSM). With export/import, you can create the tablespaces as you want them to be before the import step and get this done at the time of your database migration.
More details on upgrading Oracle databases can be found in the Oracle documentation, specifically the Migration Guide. I highly recommend reading this document as it discusses your options in more detail.