Moving a table to a new tablespace on Oracle 10g is quite easy and a straight forward task.
On Oracle 10g you can move a table from one tablespace to another as shown below. Keep in mind that everything associated with the table is moved as well (e.g. privileges, constraints, synonyms, etc.), but NOT indexes.
SQL> ALTER TABLE MOVE TABLESPACE <new_tablespace>;
WARNING: By doing so, all indexes associated to the moved table will no longer useful and must be rebuilt as the following:
SQL> ALTER INDEX <index_name> REBUILD;