make sure the tip of the new needle is touching the butt of the last needle worked before making that first stitch. i do this with circs and with dpns. doesn’t matter.
i flipped the work around so it should look as if the work is in front of you.
this was fiddly so work with me here.
click photos for full view
the new needle (2) inserted in to first stitch on working needle (in the front door)
wrap the yarn around and pull taught (grab your scarf) . the new needle (2) will touch old needle (3)