The picture shows a "socket" that will hold a normal "flanged" flashlight bulb (somewhat) securely in contacts with normal wire. I'll try to get more "process" pictures if I can find my tongue depressors, but the finished-product photo should show most of what you need to know...
Step 1: The Issues!
Traditionally, one wraps a wire a couple time around the base, which works "ok", and then uses tape to hold the nipple against the end of a battery, which works NOT so well.
Springs are good, but generally hard to find in whatever size you actually need. "Springy" metal tends to be difficult to work with. You can solder wire to the nipple, but that's a pain, not really that reliable, makes the bulb non-replacable, and isn't appropriate for younger children.