Restore the full backup to the new server and all the new archive log files that you want to restore.
See note: 161742.1 (How To Roll Forward The Database Using a Old Control File, With Archivfiles) in metalink for a complete guide but I'm going to paraphrase it.
If you do not have access to metalink then here is the text from that note abreviated:
start db in mount mode
SQLPLUS> startup mount
Issue the command to start the recovery and apply all the archivelog files that are newer than the control/datafiles restored.
SQLPLUS> alter database recover until cancel using backup controlfile;
use this command to continue until you run out of archivelog to apply.
SQLPLUS> alter database recover continue default;
when you run out of archivelogs to apply
stop the recovery and open the database with reset logs.
SQLPLUS> alter database recover cancel;
SQLPLUS> alter database open resetlogs;
its important to take a new backup now as old archive logs will not be able to be used with this db since you've reset the logs.
As stated by the other poster, read the backup recovery manual for more info.