Paint splattering is kinda messy
but try this - Get a good amount of paint on the bristles and hold your free hand over the paper. Then tap the brush against your free hand, splattering the paint on to your paper.
Easier to show than to explain, but I hope that makes sense!
You can also try using stencils for a less messy way. Or-if you have a die or punch that has splatters, cut them out and use the negative as your stencil. Brush your paint on or pounce it on (maybe with a sponge or stippling brush) to get a more textured look.