As soon as all the leaves have fallen. Dig out a hole big enough to take a good root ball, carry the tree (with help) on a piece of plastic sheet, work in a little compost round it, fill in with soil you have dug out. Tread round to firm it in. Stake and tie if it is a tall one.

And as I always say to everybody that posts this question, Japanese maples hate root disturbance, and you do stand a good chance of losing it.