Take a cold backup or hotbackup from the server you want to copy from

Install Oracle on the server you want the database to be copied to. Make sure both the versions are same.
Take the text based controlfile.

Then copy all the Logfiles, initOra file, DBF files and controlfile and ARCH logfile if in ARCH mode(Hotbackup).

Do modifications to reflect the new Db name and path names of the new server.

Then startup with the new modified controlfile.

You should be OK.