I have a love of buttons and dangly earrings. It was only a matter of time.
You don't have to use buttons, I just like them because the holes are already pre-punched. =)
First, cut your chain (or string, if you like) to whatever size you desire. I just used scissors, but you may need something sturdier depending on the thickness of your chain.
Then thread it through the button, like so.
Next, thread either end of the chain onto a jump ring.
(Please forgive my sub-par photography! xD)
Then thread your earring hook onto the jump ring. Take your pliers and close the jump ring.
(Best to hold it up and see how it hangs before closing the jump ring - it's no good having an earring that faces the wrong way around, as I discovered).
Then you just repeat the process for the other earring - ta daaah!