The next 5-15 days are probably the best window of opportunity during the entire year for transplanting trees, shrubs and perennials.  Now that the ground has thawed in most places, you can dig wide enough and deep enough to capture a generous amount of the root system so that when you re-plant in a new location there will be enough roots to allow the plant to re-establish.

Try to make sure you dig up and move your plant materials before they leaf out.  This reduces the stress on the tree, shrub or perennial, allowing it to produce new leaves and new shoots in sizes and amounts that are in balance with the ability of the plant to maintain.

Keep in mind that the more good condition roots you are able to harvest when you move your plant materials, the better the plant growth upon re-planting.  Avoid re-planting deeper than the level at which the plant was growing in its former location.  If the plant is wobbly, stake it for one growing season only, to provide support rather than planting it deeper.  When planted too deeply, transplanted trees, shrubs and perennials may do well briefly, only to decline in vigor in subsequent years.

Mulching your new transplant is always a good idea.  It will help retain moisture, keep away grass/weed competition and will help avoid mechanical injury.