Well, people *usually* access Oracle on a remote machine. In production systems, it is rare (and kind of silly) that you have a database server installed on your own PC, along with other software products you often use.
Therefore, as you are starting SQL*Plus, you must have (at least) Oracle (client) on your PC. That's fine. Now locate TNSNAMES.ORA file and create a database alias for the remote database. If you are uncertain of how to do that, ask the DBA for the details. He/she might even send it to you. Because, it appears that you don't know SERVICE NAME. Your entry might look like
The rest is easy: don't connect as "sysdba", connect as user whose data you'd like to modify within the SQL script. For example: if there's the "TEST" table (copy of Scott's "DEPT" table), here's a sample TEST.SQL