Wire wrapping with headpins is a simple technique that you can master relatively quickly. I found this good tutorial online, and you can find others if this one doesn't work for you.
In my opinion, you can do this without the bent nose pliers, and in the video the craftswoman says that chain nose and needle nose pliers are the same thing. Beware! This is not true, chain nose pliers, and any pliers you use for wire wrapping, must not have teeth. If you try to do this with needle nose pliers that have teeth, you will make a mess of your wire and could scratch your bead or other element. Otherwise, I support the technique displayed here.