A week before you move you should treat your plant for pests. Place your plant in a black plastic bag. In the same bag place a bug/pest strip, conventional flea collar or bug powder. Then close the bag and place in a cool area overnight. This will kill any pests on the plant or in the soil.
When you prepare your plants for move place them in cardboard boxes and clearly label DO NOT LOAD so they won't mistakenly be taken on the moving van. Cushion the leaves with wet paper towel and place a final layer of wet paper towel on top to keep them moist. Before loading into your car close the boxes and punch air holes in the top. More information on public storage here.
When moving plants to your new residence via your car, try not to let foliage rest against the windows, as the leaves will scorch.
The plants should be unpacked as soon as possible after arrival. To avoid breaking the stems, remove plants through the bottom of the box. Initially, do not expose the plants to large amounts of light. Allow them to gradually become accustomed to more illumination.
