Do you know how to install Oracle on the new server?
Good, install it.

Do you know how to back up your database?
I hope so. Back it up and restore the database on the new server.
Then start the database. If you are installing on Windows you will need to create a service, which you can do at the dos level. On Unix you have to put the right files in the /etc directory. You can find this in the before you install guide for your platform.

Then configure your listener. Of course you don't mention what version of os you are running, whether or not you are changing Oracle versions and what they are. Unless your database is huge, it should be a simple thing to move the database.