How to export all tables with user in Oracle 10g Enterprise edition?
You can use Oracle Datapump to perform export-import in schema(user) level. 

Here are some examples.

expdp scott/tiger schemas=SCOTT directory=TEST_DIR dumpfile=SCOTT.dmp logfile=expdpSCOTT.log


The above command exports SCOTT schema in a dump file called SCOTT.dmp in a directory specified using DIRECTORY parameter, and writes it's log in expdpSCOTT.log file.

You can copy this dump file to another host and use Datapump Import to import it as shown below.

impdp scott/tigerschemas=SCOTT directory=TEST_DIR dumpfile=SCOTT.dmp logfile=impdpSCOTT.log


References:
Data Pump Export
Data Pump Import
CREATE DIRECTORY