Call all your local utility companies, not just the electricity provider, to mark the location of underground pipes and cables in the section of the landscape where you'll be working. Also ask the electrical company if there are any setback requirements for plantings near the transformer box.
Contact your local municipality to check on regulations for planting near electrical boxes. If the box is near the front property line, there may also be restrictions on the types or heights of plants allowed near the sidewalk.
Measure the area around the utility box and draw a to-scale diagram of the existing features, including underground utilities, existing plants and fences and the box itself. Be sure to mark off any required easements. For example, the electric company may require you to leave the side of the box with the doors unplanted. If you also have overhead wires, mark them as well.
Draw line-of-sight guidelines so you know where the main screening should be. If you don't want to see the electrical box from the dining room window, for example, draw a dashed line from the box to the window so you site your plants accordingly.
Draw the outline of the planting area and roughly sketch in groups of plants -- for example, a mass of shrubs or some ornamental grasses. Don't decide on individual varieties yet. At this point you're just trying out different combinations to find a pleasing arrangement that also takes the focus off the box. Give the outline of the bed a simple, graceful curve.
Choose a variety of plants that are suited for the growing environment near the box. Include both evergreen and deciduous shrubs for year-round interest; if you have enough room, leave spaces where you can add seasonal flowering plants or perennials. Include a small tree to act as a focal point to draw attention away from the electrical box. If the transformer is far enough from the house to make watering impractical, use plants that are drought resistant.
Prepare the planting bed and install the plants. Use tillers with caution, since it's easy to misjudge how deep you're digging. Use a shovel and dig slowly and carefully near marked underground utility lines and pipes, and don't place shrubs or trees directly over them. Space your plants far enough apart that they'll be properly spaced when fully grown.
Spread a layer of mulch over the entire planting bed and around the utility box to conserve water and discourage weeds. Renew the mulch yearly.