To get a script for private synonyms owned by a particular user, go to Schema Browser-Synonyms and set the filter for “Private” and “Current Schema Only”. Then select all of the synonyms out of the Schema Browser and get a script for them.
If you have Toad Professional or DBA module, then you could go to Database | Export | Generate Schema Script to extract a script for a user, plus all objects (or objects of a particular type) for a given schema.