Decide what shape you'd like your luggage tags to be. You can go with the traditional style like they have at the airport, or you can choose your own shape. You can use either plain manila paper or colored. Cut enough tags to cover all the bags that will be going on the trip.
Once you have the tags cut, pick the end from which you want to hang from your luggage. Take the hole puncher and punch a hole in that end. It's best to punch the hole before you do any writing; that way, you know how much room you have for information.
Write your information on the tags. Make sure you include your full name, home address, and phone number. The point of luggage tags is that, in the event a bag gets lost, your bag can be returned to you. If you have a laminator you can run the tags through at this point. You'll need to trim away any excess lamination and re-punch the hole as well.
Tie the elastic string to your tag and attach to the luggage. You can go to any craft store or even a Wal-Mart to find elastic string in any color you want. Make sure you tie the knot securely so it doesn't come loose during the trip. By using elastic string, it will be easier to take the tags on and off if you so choose. If you will be leaving them on permanently, you don't have to use elastic string.