Water the Dracaena marginata plant thoroughly before transplanting it. Pour 1/2 cup of water into the planter for every inch of depth. For example, a 6-inch-deep pot requires 3 cups of water.
Prepare the new planter while the water drains from the Dracaena marginata plant. Choose a new planter with a 2-inch size increase and at least four drainage holes. Find one with an attached drainage basin at the bottom, if possible.
Combine 2 parts potting soil, 1 part peat moss, 1 part medium-grit sand and 1 part perlite to create a good all-purpose growing mix. Pack the bottom quarter of the new container with the growing mix.
Remove the Dracaena marginata from its original pot. Place your hand flat against the soil around the base of the plant. Tip the pot and let the rootball slide out onto your hand.
Remove approximately 1/4 of the soil from around the roots of the Dracaena marginata. Discard the soil and do not use it for potting other plants.
Hold the Dracaena marginata in the new planter so the base of the trunk stands upright and rests 1/2 inch below the edge. Pack the soil mixture created in Step 3 around the roots of the plant.
Shake the planter periodically to settle the soil. Keep adding soil until the planter is filled and the surface of the soil is even with the base of the Dracaena marginata plant's trunk.
Pour 1 to 2 cups of water onto the soil to settle it. Add additional soil to maintain an even surface, if necessary.
Place the transplanted Dracaena marginata plant under the same conditions as before. Withhold further watering until the top 2 inches of soil dry out.