Its very simple.
Take the latest backup of the database in any shared directory on the same server.
Copy the backup to the new server where you want to restore the database. Restore it using Enterprise Manager or SQL Query Analyser.
If you are restoring transaction Log backup be sure that you are attaching all the logfiles in the same sequence they were backed up followed by completed database backup. Also keep the database non-operational while restoring transaction log backup.
Thanks and Regards
Ritesh