A lot of people have mentioned the importance of "pre-drafting" fiber before spinning it, especially for beginners. And I did correctly understand the term to mean "loosening up the fiber" so that it is easier to draft while spinning. I gave it a few tugs, until I felt the fibers begin to separate, and then started spinning.
And then I read about pre-drafting in Spin to Knit. As it turns out, my understanding of pre-drafting was a little off. According to the book, this is how you pre-draft.
First, you pull off a strip of fiber from the roving. It looks like this:
Then, you pull it apart gently from side to side, to get this:
Finally, you stretch it vertically, to make a long, narrow tail-like creation, like this:
And then you can spin it.
And you know what? It works!
My yarn may still be uneven, but it's definitely much, much finer. Now, if I can just figure out how to get it off the bobbin without it untwisting...