First - buy from a reputable nurseryman and look for a well filled (but not pot bound and suffering) pot! I'm using a Primula vulgaris cultivar as an example here. Most can be torn apart and potted up in this way from late winter until early summer!
Knock the plant out.
Carefully tease the rootball apart.
Separate into individual plants for potting up.....
Job done!! You got your three plants plus an insurance pot!
An example of the tips and tricks covered in the popular talk 'Propagation - a matter of life and death'