1. If the batt is basically the same throughout, the easiest way I have found to spin from it is simply to tear it into strips and spin one strip after another just as though it were roving. This method also works well for striped batts where you want the yarn to follow the same pattern as the batt. For example, here's a striped batt that I made and named Rhasberry Truffle:
I actually made several striped batts, tore them into strips, and then I spun this yarn from them, spinning each colored stripe separately and then plying it back to itself:
If you're wondering why I didn't just card the colors separately and then spin a handful of each, it's because I had planned to sell the batts, but they just kept calling to me to spin them :-) and I couldn't resist! The yarn is for sale at my Etsy shop here:
2. If you prefer not to have to start and stop to combine pieces, one way of turning an art batt into what is basically a long roving is to make it into a "W." In this case, you would tear a strip most of the way, but about an inch or 2 from the end, turn the batt around and begin tearing the other direction. Fellow Etsian, AtomicBlue, shows this method in a Youtube video here:
Both the strip method and the "W" method are good for batts that are either the same color variations throughout or for batts where you want the colors to change as they did in the batt.
3. If you have a multicolored batt where you want to maintain all the colors throughout the whole batt, my favorite method is the one that Deb Manz demonstrates in her video here:
Basically, the method is to lay the batt out on a flat surface and pull gently until you see the fibers move. If you pull too hard, the whole things comes apart. Then you do the same thing again with a small section of the batt by placing your hands about 6 inches apart. Keep doing this along different sections of the batt until the whole thing is the width of roving you like to spin from, which varies depending on how bulky or fine you want the yarn to be. It's rather time consuming, so I only do this if I want fine color variations rather than broader ones. If it does break while you're doing this, it isn't a big deal. Then you just have 2 rovings to work from in the end instead of just 1 roving. I highly recommend her video by the way. She's an excellent teacher.
I know there are other ways that people use to spin from batts such as treating the batt as a giant rolag or spinning from the fold. It's amazing how different the effects can be depending on the method you use, and I think when you get or make a new batt, the first step is to think about how you want the yarn to look and choose the method that gets you there.