When you take your new length of yarn out from under the spindle's hook, keep a medium tension on the yarn. I usually hold onto the end of the yarn just before the roving with one hand, while the other hand holds the spindle.
If you relax this hold, the yarn will want to wrap around itself along its length, curling up. That is because the fibers want to be in a relaxed state, not holding all the twist you've just put in them. This is a "good thing" -- when you ply, you'll take advantage of this desire of the fibers to twist around each other, to create a strong, balanced yarn.
But when you are winding on, you need to maintain an even tension so ensure that the snarls and curlies don't get into the wound-on yarn ("cop") already on your spindle and make your cop uneven.
If your length of yarn makes this arm's length's hold impossible or even just difficult, use the Peruvian butterfly wind-on to keep your yarn under control while you wind it onto the spindle.
What you will learn to evaluate as you progress in spinning, is whether you have a good amount of twist in your singles based on how you want to use the yarn. The trick is to fold a 4" length back on itself and let it curl naturally -- this shows you what your balanced 2-ply would look like (this is the ply-back test). Do you like it? then you have a good amount of twist in there. Is it really poufy and has an open loop at the bottom? then you could add more twist. Is it really tight, so the twist on itself seems almost cork-screwy? then you might want to take some twist out.
If the fiber is corkscrewing on itself even as singles as you are spinning, then it's extremely high twist -- typically this level of twist is used only in specific circumstances, art yarns, crepe yarns that sort of thing. If you can't put less twist in (that spindle moves awfully darn fast at first!), then take some twist out until the corkscrews disappear. Nothing says you can't unspin your yarn a bit before you wind it on.
For other posts about spindles, see the Spindles category (hosted by del.icio.us).
Are you just learning to spin on a spindle or wheel? Have a question about what you are seeing or doing? Feel free to post a question in a comment on the blog or contact me. Thanks!