There was a bug in earlier versions of Oracle on AIX that caused SYS_GUID() to generate non-unique IDs so if you're still on an older version and using AIX, check this Oracle Support Note first: DUPLICATE SYS_GUID generated on AIX can lead to ORA-1 errors during enqueue (Doc ID 1371805.1).
Ok so triggers are a little bit like PL/SQL, but you don't have to worry about calling them, just create the trigger on a table and you're done. In my example below I assume that there is a table with the name MY_TABLE which has a column named MY_UUID of type VARCHAR2(36) that will hold the UUID.
Here's the code for the trigger...
This trigger is created so that it adds the UUID value on each insert. A local variable, l_sysguid, is used to hold the output of the SYS_GUID() call, then SUBSTR() is used to split up the value into separate parts as required for a UUID and append them with dashes.
The output of SYS_GUID() looks something like this...3F0900B5E3783798F2E0302D7120A3DF. That is a unique value, but not necessarily a RFC 4122 type UUID, but it doesn't need to be. The logic in the trigger converts all the hexadecimal letters to lower case and then creates a value would look something like...3f0900b5-e378-3798-f2e0-302d7120a3df.
Pretty simple and it works well.