Scoop a small amount of acrylic grout onto the end of the grout float. Because you are working vertically and the acrylic grout is thinner than cement-based grouts, use only a small amount at a time to prevent it from running or falling off the wall.
Press the tip of the grout float against the top of a grout joint on the backsplash at a very low angle to the wall. Hold the float between 30 and 45 degrees from the vinyl tiles and drag it downward to press the grout into the joints. Drag the float only over the joints, not over the entire tile.
Press the grout into the joints between the tiles from various angles to help ensure complete coverage. Hold the float closer to 90 degrees and scrape down the tiles where grout has covered them to help direct it close to the joints. Take care not to scrape the grout back out of the joints; vinyl tile joints are extremely shallow.
Allow the grout to dry for 10 minutes to help set up the joints. Slightly dampen a sponge, and gently clean the excess grout from the tiles. Work carefully around the joints and rinse the sponge frequently to keep the installation clean. Let the backsplash dry for 24 hours before reattaching outlet covers.