Prepare the surface to be painted. If you are going to paint directly on a wall outside, repair any cracks in stucco, concrete or brick. If the surface has been previously painted, try to find out what kind of paint has been used. Acrylic tends to bead off or peel away from surfaces that have been painted with oil-based paint. Brush a little of your primer on it and see if it will stick. Let it dry, and see if it peels away. If it peels, you may want to rough up the surface using sandpaper or paint the mural on a large piece of exterior plywood and mount it on the surface.
Apply the primer and allow it to dry. It should seal the surface to be painted but not peel away. If you are painting a landscape or will have another large background, mix a little color from your tubes of acrylic with the second coat of primer to help out the picture-painting process. For example, while the primer is still moist, squirt some cerulean blue along your planned skyline. Feather it upward with a painter's sponge or a fan brush. If you are using an airbrush, lay down a dark layer of blue near the skyline then use a lighter and lighter spray as you move away from the horizon upward toward the top of the picture. As soon as this layer dries, thin a little titanium white with water in a paper plate until it is a thick soup. Rock a natural sponge in the paint, and daub lightly onto the sky area to create clouds.
Sketch or project the picture onto the wall. An opaque projector can really speed up this part of the process by throwing the picture you wish to reproduce on the wall and allowing you to quickly size the projection to the required space. You can then draw the outlines of the spaces in the picture on the area to be painted. Failing that, you will need to either freehand the drawing onto the wall or transfer it using a grid.
Paint the background portions of the mural first, then fill in the foreground and details. You will need to pick a time of day when the sun will not warm up the surface of the painting too much, and when it is not cold or wet. This may give a sort of hurry-up-and-wait quality to your painting time. Acrylic paint dries very quickly. If the wall is warm, there will be problems with spreading the paint. If the wall is damp, acrylic paints will not bond well to the surface and the picture will chip and peel. An ideal painting time is when the wall is lightly shaded, but the surface and surrounding air are warm and dry.
Use similar methods to create the foreground. If creating a landscape, greens will become darker as they near the horizon, becoming purplish with distance. The immediate foreground should be much lighter. Add details using smaller brushes and sponges. Clean implements between colors; have plenty of water and paper towels on hand for this part of the process. An unbreakable container or two half-full of water is a good place to rest brushes, sponges and other implements between uses. On a hot day, acrylic can dry rapidly enough to damage delicate art equipment.
Paint bold abstract paintings using various sizes of paint rollers. Paper plates are excellent trays for small bristle painters and small paint rollers. Again, work quickly and keep tools moist. Texture broad surfaces by dipping a toothbrush in a contrasting or complementary shade of paint, and scraping back toward yourself with a flat implement, such as a ruler or ice cream stick. This will cause droplets of paint to fly out in front of you onto the painting.
Protect the complete painting by spraying or brushing a clear acrylic finish over the completed picture. Be very sure that it is an acrylic finish; some types of clear finish mix poorly with acrylics. In an area where the picture may be subject to blowing dust or sand, you may want to apply three or four coats of protective finish. Let each coat dry before adding another.