Pour 1/4 cup of all-purpose cleaner in 1 gallon of water, and mix thoroughly in a bucket. Saturate a sponge or rag into the cleaning solution, and wring it out. Wipe down the walls to remove dust, dirt and debris. Allow the walls to dry thoroughly.
Pour white paint into a roller pan. Dip the roller's nap into the paint, and apply it over each wall until completely covered. Allow the paint to dry thoroughly, and repeat the process with another coat of white paint to form a solid base coat.
Measure the horizontal distance from one corner of a wall to the other to determine the spacing between the pinstripes. Divide the measurement in inches by the desired spacing between stripes to calculate how many stripes you need for that wall. For example, if the wall's width is 96 inches and you want the stripes spaced 4 inches apart, divide 96 by 4 to determine the total number of stripes, which equals 24.
Measure and mark the location of each stripe along the bottom of the wall with a pencil. Using a sturdy stepladder or stool, also mark the locations along the middle and upper edges of the wall. Join the spots on the wall to form vertical lines. Use a level to check that each pencil stripe is vertical, or adjust if necessary.
Run a length of painter's tape on either side of the pencil stripes along the wall in the desired width of the pinstripe. Pinstripes are narrow, so measure an equal spacing on each side of a pencil stripe, and mark with tape. Ensure the stripes are identical in width.
Apply navy blue paint between the tape using a 2-inch paintbrush. Allow the paint to dry thoroughly before removing the tape.