If you’re using a pendant that you didn’t make yourself you may be more limited since you won’t be able to "build the attacher into" the item, but there would be many ways to add things, drill holes, etc., in many different materials.
You may be somewhat limited by the type of material your pendant is made from though in some cases, and/or how *you* want your finished strung item to look.

Some possibilities would be drilling holes, adding eye pins or u-shaped or coils or tubes or bails or something else (using glues or other attachment methods) and using jump rings or other attachers for some of those, wrapping with wire then attaching to the wire, adding a back which has a loop or some kind of attacher, soldering attachers onto metal pendants, etc, etc, etc.

You might want to check out some of the possibilities on the Pendants page of my site to get started:
http://glassattic.com/polymer/pendants_cording.htm
And these two pages will have more ideas about various ways to make holes in beads (since your pendant could be considered a large "bead"), and about various ways to use wire to make attachers yourself:
http://glassattic.com/polymer/beads-holes.htm
http://glassattic.com/polymer/wire.htm

My site is primarily about polymer clay (many people use it to make jewelry as well as for other things), but many of the ideas on those pages could apply to many other materials as well.

HTH,

Diane B.
References :
http://glassattic.com/polymer/contents.htm