The ones in the video below use a couple of specialized items, but the instructions can easily be used as a general tutorial that can be adapted in different ways to suit one's needs. And for those of you who are into scrapbooking, you may already have the supplies on hand.
The card holders she mentions are inexpensive and readily available on Amazon or in stores. However, an alternative might be to use self-adhesive laminating sheets, clear Contact paper or even (if you made the tags small or long and narrow) clear packing tape.
There are also alternatives for fasteners ranging from bead chain to plastic loops to various kinds of key rings readily available in bulk at craft stores.
Designs could be handmade or printed on a computer. And, of course, there are other alternatives. I saw videos and/or tutorials of tags made from Sculpey clay, from Duck brand duct tape and, of course, ones that were sewn (with the name and address info written on white backing with fabric pens).
It's the kind of thing that can be elaborate or very simple and, if you don't want to use them as the main gift, might be affixed to a package as both a gift and a gift tag. I'm enjoying coming up with some fun ideas. Let me know if you have others alternatives to what is suggested above.