When you have finished the decreases at the top of the hat you will be left with a relatively small number of stitches. You will leave them on the needle and cut the working yarn, leaving a long tail. If the hat is knit flat, you want your working yarn tail (the one you’re cutting) to be long enough to be used to seam the hat. If working in the round, the tail only really needs to be as long as is necessary to properly weave in the ends once completed.
So, this is how I would follow the instruction. I would thread the cut end through a tapestry needle, then carefully transfer each stitch off the needle and onto the tapestry needle, pulling the cut yarn through the stitches as you go. Also something you can do is leave a little loop of yarn on the right side (the side you started transfering stitches from) and thread the tapestry needle through the loop before you pull it tight.