On Oracle, if it turns out your database character set is wrong...
First, you need to run the 'csscan' utility (in $ORACLE_HOME/bin) to check whether you've got characters in your database that would be affected by a character set change. If you have, you need to deal with them yourself - there's no 'magic wand'!
Once you've verified this is okay... you can change the character set of an Oracle database with an
ALTER DATABASE CHARACTER SET <new character set>;
So in your case, you'd *probably* want to do:
ALTER DATABASE CHARACTER SET AL32UTF8;
As you're (probably) changing from a character set that is a subset of UTF8, then you shouldn't hit too many problems.
By far the safest method is to do a full (datapump) export, (re)create a new database with the correct character set, and then re-import.
A longwinded process indeed, but it does ensure that you only make this mistake once
PS: Please make sure that you know what you're doing before you change character sets! And if it's live - backup! backup! backup!