Handspindles are a wonderfully portable and an inexpensive way to start spinning. But some people get frustrated because they are awkward to get yarn off. A few simple items will make a lot of difference.
If you use the same spindle most of the time, it's frustrating to wind yarn off into a ball all the time when it gets full. If you wind onto a paper quill, you can just slide it off, make up another quill, and keep going. Also, your yarn is already on a nice bobbin that is easier to work with than a bunch of balls.
You can make a quill out of any kind of paper as long as you can wrap it tightly around the shaft of your spindle. I use a square of waxed paper from the kitchen. Wrap it around your spindle and tape down the end so it is smooth and tight. Don't tape it to the spindle, because you want to be able to slide it off later. When you wind on, make sure your yarn stays on the paper by winding it in layers away from the whorl. Make a smooth tightly wound package that tapers on both ends so it will wind off nicely.
When you fill the quill, slide it off the spindle and start another. You can ply directly from the quills by making a plying box. Find some knitting needles or wood dowels that are smaller than the shaft of your spindle and a narrow cardboard box. Punch holes in opposite sides of the box so the knitting needle sticks out both sides. Slide a quill on the needle so you can unwind it. You can also use other kinds of bobbins, like empty cardboard tubes. And if your spindle fits, put it in there too. If you plan to unwind directly from spindles a lot, cut a slot from the top edge of the box instead of just punching a hole. That will make it easier to get the spindle in and out, but be careful to not pull the spindle out along with the yarn. If you want to get really complicated, cut at an angle and pull from the other direction so the spindle can't go anywhere.
Now you can ply from the box. To help it unwind nicely, use a hook above the box to guide the yarn.