You could do a variation of this project to include the microphone and one button remote button, but if you do that, make sure you have a jack with 4 collars to connect all the wires. Another, easier variation is to use wider paracord that fits over the insulation so you don't have to strip the wires at all. These instructions assume you're using the same kind of earbuds I did, so you may need to alter it to fit your supplies.
Step 1: Materials and Tools
a few feet of 2mm paracord (not the standard 3mm)
old headphones or two old single-speaker earbuds
a 3.5 mm jack (Be sure to use the jack size that fits your phone. Also, you can use the one from existing headphones if you're OK with soldering the wires back together)
shrink wrap tubing
a lighter or matches
something sharp and pokey and/or flat and pokey
Step 2: Step 1: Strip the Insulation From the Old Headphones
Cut the existing jacks off the earbuds
Pry the microphone case apart with a small flathead screwdriver and disentangle the microphone cord from the speaker cord
pull the cords out of the microphone case so all you're left with is the lone speaker cord
strip the speaker cord leaving an inch or two of insulation close to the speaker
test the speakers to make sure they still work
The most successful method I found for stripping the wire, and this is kind of embarrassing, was to bite off the insulation at one end, split the insulation lengthwise, then pull the insulation away from the wires. I also tried using the wire strippers with some success. If you do that, strip of only a few inches at a time, and try not to stretch the wires too much. If you want to know why, read The Strand by Stephen King.
The speaker wire strands are coated, so you'll have to get that coating off in order to test them. To do that, burn the ends of the wires for a couple of seconds so that you have 10 mm or so of naked wire. To test the speakers, plug the 3.5mm jack into a music source and connect each speaker individually. If you hear music, they're good.
Step 3: Step 2: Prep the Paracord
Step 4: Step 3: String the Wires Through the Paracord
Take a length of fishing line more than twice the length of the longest length of paracord and fold it in half, putting a sharp crease in it. Starting with the shorter length of paracord, push the folded fishing line through the paracord, crease first, until it comes out the other end. Feed a couple of inches of the jack-end of the wires from one speaker through the loop and then pull the fishing line back through the paracord so the wires are all the way through. Snug the paracord up to the speaker, and if you want to, put some shrink tubing over the connection to keep it together (I skipped that).
If you plan on using shrink tubing at the connection between the paracord and speaker, you'll have an easier time on the longer length if you thread the tubing first.
For the longer length, string the fishing line from the slit you cut in the middle of the cord up to the top where the speaker will be. Then pull the wires of the second speaker through so that the wires exit the slit. Snug the paracord up to the speaker.
For the lower part of the headphones, string the fishing line up from the bottom through the slit in the middle of the longer portion of cord. Loop all four speaker wires through the end of the fishing line and pull them through. Test them to make sure they still work.