firstly you need to wate till the trees/shrubs are dorement ie winter . you have 2 windows of opertunity . one is very late autumn and the other is very early spring . there are plusses and minusses to both ways . personaly i replant or move them in very early spring so any damage or stress is soaked up bye the spring growth rather than sitting threw who knows how cold a winter in shock for 4-6 months . i hope that helped .

AS NP says in general late autumn or early spring. But there are exceptions, for example rhododendrons should be moved now. So it really depends which shrub/tree you are referring to.