I'll assume you are not using an RMAN catalog, but you have a pfile ready to go on your new host.

Step 1 - you need to set your DBID. You can find this in the log files for any of your backups. If you don't have them (well...I'd fix that for the future) then it is still possible to find it by doing some binary analysis of the backup files, but you really don't want to be going there :-)

set dbid=123456789
startup nomount

Step 2 - you get a controlfile from your backups

run{
  SET CONTROLFILE AUTOBACKUP FORMAT FOR DEVICE TYPE DISK TO '/u01/mybackup/location';
  RESTORE CONTROLFILE to '/u01/app/db/my_control.ctl' FROM AUTOBACKUP;
  ALTER DATABASE MOUNT;
}

Step 3 - Now that you have your control file, it contains the information to get your database back. If the backups are in the same location on the new host, you're good to go, otherwise you might need to run CATALOG commands to let RMAN know where the backups are now located. But then you restore and recover like normal

run {
  RESTORE DATABASE;
  RECOVER DATABASE;
}

There are various scenarios in the docs that have variations on the above, but the most important thing is that you practice these things regularly. As the old saying goes:

"A backup is not a backup unless you know how to restore it"