If you want to get list of grants made to tables and you want to recreate the user permissions in a different environment, the easy way to generate a script is to use the dbms_metadata.get_granted_ddl function as described here. However, if you do not have DBA privilege on the database you will not be able to use that method. Here is a simple sql that you can use to generate a script that will work in most common situations. This just relies on the TABLE_PRIVILEGES table.
select replace('GRANT ' || decode(select_priv,'Y','SELECT','') || decode(insert_priv,'A',',INSERT','') || decode(delete_priv,'Y',',DELETE','') || decode(update_priv,'Y',',UPDATE','') || decode(references_priv,'Y',',REFERENCES','') || decode(alter_priv,'Y',',ALTER','') ||' ON '|| owner || '.' || table_name || ' TO ' || GRANTEE ||';','GRANT ,','GRANT ') from TABLE_PRIVILEGES where owner= 'OWNER' order by table_name, grantee;