Wait til after flowering, take the biggest rootball you can, if possible put it in at least filtered light or somewhere that gets a little midday shade, and keep well watered.

Dig a hole - which may need altering to fit the actual rootball, instead of the imagined rootball - before you begin to dig the tree. Water the cherry well the day before you dig it - you don't want mud, but you do want the tree to be well hydrated, and you want the root ball to stay together as much as possible. Use use a tarp to shift it, don't pick it up by the trunk, handy as it is, as that can disturb roots. And mulch it.... Oh, and try NOT to do this when the hottest days of the year are forecast - an overcast day would be good and the day before rain would be perfect.