Paint Splatter Effects are super easy with Illustrator symbols, he advantage of those presets is things can be changed in seconds from a background of spots and dots to a background of stars or cube or any other paths. You can apply a presets that looks like paint or pencil sketches or made up of type and fill the screen in seconds.
The symbols panel can be found in the window menu. You can add all kinds of color to the spot design as well as add live effects so go to the effect menu and stylize and drop shadow and click OK. Drag the design into the panel. Select the default dynamic or static, export type doesn't matter and give it a name. Goto the toolbar and select the sprayer tool. You could also make additional designs as well such as a blurred design or a multi-shape artwork or a distorted one, save them all to the presets panel and you can then select them instead of the basic spot design. You can make far more complex designs that way.
Apply the dot spray by selecting the preset in the panel and applying to the art board. You can add more and more to the group of instances. You can also edit the source design and change it at any point by double clicking the preset. You can apply the sprayer in any part of the image or fill the entire image with your design
At present, it doesn't look much of a splatter but you can apply the sizer tool (on the same tool as the sprayer) to re-size the dots. Just hover over the dots that you want to re-size, hold down the alt or option key to decrease the size. You can also use the shifter tool to move the items around, perhaps bunch them closer so they look more like a blots and dots and not just spaced all over the art board. With the shifter, just drag them all closer. When you drag the design to the panel to save the art, you can save it but, sadly, it is expanded which means it loses the live element. I would suggest saving a backup of the design in a separate AI file or just on the art board if you want to change it or save it to the CC libraries via the libraries for future use, you can also then use the artwork in applications such as After Effects and others.
Select the new preset in the panel and then use with the sprayer and again you can apply it over and over as well as add in re-sizing using the sizer as well as rotation by using the spinner as well as color via the stainer tool (if you want to stain it with green then set the fill color in the toolbar to green).
If you kept the original design before adding it to the panel then you can edit that design. If you haven't, you will have to go back to the original spot or source design and change that to a new artwork. You could go for a star effect instead. Double click the design in the panel and then change that. Any changes made to the symbol will change in all the instances. As before, you can then drag this design into the symbols panel. Select the new set and then apply the design using the sprayer and re-size using the sizer etc to create your design this time based on a star, though the artwork could be of anything and even different shapes