You want to get a blunt needle with a big eye on it. You can buy packs of “braiding needles” from a tack shop, but I’m sure there are cheaper options from sewing supplies. Just don’t use a plastic one–worthless.
And then you will need waxed thread in the color you want for your mane. If the ends are not too blunt cut, I don’t bother with tucking the tail up and wrapping around like in this video, just go through the end with the thread a couple of times. If you’ve blunt cut the mane, then it can be hard to braid all the way to the bottom and you may have extra hair you’d want to tuck out of the way.