Prepare your wall for painting by wiping it down with a sponge and mild liquid detergent. Apply white interior latex paint to the wall for a clean, bright background. Paint the wall sandy yellow or sky blue if you want to create a tropical beach background.
Practice drawing palm trees on paper to familiarize yourself with the shapes and proportions of a palm tree.
Stand back from your wall and look at the space you have available to paint your palm tree. Work out roughly how big you want it to be. Lightly draw a rectangular shape on the wall with pencil or chalk. Keep within the lines of the rectangle when creating your palm tree.
Draw the outline of your palm tree on your wall with chalk or pencil. Begin with a line several inches long, on a slight diagonal, for the base of the trunk. Exactly how long the line is depends on how large your palm tree is to be.
Draw a second horizontal line above and parallel to the trunk's base line. Make this line a tiny bit shorter. Repeat with several more lines until the trunk is finished. The trunk should taper very slightly from bottom to top.
Draw the branches. Make a line from the side of the top of the tree, slanting outward. Make a second line, leaving a generous space between the two lines. Continue drawing branches until you have eight in total, creating an octagonal shape over the top of the tree.
Draw leaves coming off each branch. If you do not want to paint individual leaves, draw a zig-zig shape around each branch. Each point represents the tip of a leaf.
Paint your trunk brown or tan with a 2-inch paintbrush.
Paint the leaves in one color of green for a solid, simple palm tree. To add more detail, use two or three different shades of green, such as dark green, olive green and yellow green. Decide where the sun would be in your image and paint patches of the leaves in the lightest shade of green where they would be in direct light, with the darkest shade on the underside of the leaves to show shadow.