You could spin directly from the batt, but that's a heck of a lot of fiber to have sitting in your lap, and if you have a pet, it's really not a good idea. Your pet, especially if it's a cat, will like that fiber just as much as you do (or maybe more!)
The first thing you should do is to divide the batt into manageable amounts to spin from. You may not want to do this all at once, for there's many ways to divide up the batt, and each way produces a different result. You could divide the batt by color:
The above is only half a batt, for I'd divided the batt this way beforehand:
There's no special technique for ripping a batt up. You simply grab the batt with one hand, and pull the fiber off with the other.
As you can see, this batt had gotten rather beat up and compressed, but that's not a problem, for one can then attenuate the fibers. You can go ahead and spin without any more preparation, but if you do the next simple step - attenuating the fibers - you'll find spinning to be a breeze.
Attenuating simply means pulling the fibers apart. Again, you hold the fiber in one hand, and pull with the other. Do a handful at a time. In the end, the fibers will look like this:
Here's some I did last night, with colors from another batt. You can see that this one is not nearly as neat:
I put my foot in the picture (and not in my mouth), so you could get a sense of scale.
Let's go backwards and see how this one started. I was quite sloppy about ripping this batt, as you can see:
One handful of fiber ripped the short way from a batt will give you quite a lot of fiber to spin with! I spun 24 yards of singles thick enough to produce a worsted weight yarn when plied:
There's many ways you can divide and use your batt. Attenuating the fibers neatly, as they are in the picture with the purple fleece above, will provide you with the easiest spinning experience. If you do a more sloppy job, you'll have to do more work when you're spinning to create a consistent yarn. On the other hand, being more loose about attenuating the fibers can assist in creating a more "rustic" yarn, with all the nice lumps, bumps and slubs that say "hand spun" without using any fancy spinning techniques.
There's plenty of fiber in a batt. If you've never used one before, it's a great opportunity to learn and play.
Here's a close up of some small skeins which were made from various batts, including the twelve yards of plied yarn from the singles you've already seen:
Except for the green and blue skein, these were all made from the fiber that was left on the drum carder after a batt was made. You can create yarns that look just like these if you use handfuls of your batt in a rather random fashion. There's so many possibilities when spinning from a mixed batt. You can be very deliberate about how you divide it up, using a scale for precision (!), or you be just the opposite by closing your eyes and pulling off random handfuls. . .it's entirely up to you.