For now, just wait. It's hard to tell how far it may have died back.
If the wood has died back to main stems, the tree will have to start
new budding tissue from that area. You can take a pocket knife, strong
thumbnail or the side of your pruner blade and gently scrape the outer
bark from a tiny area, checking for green tissue under the bark
layer. Continue doing that down the branch until you find some
color. If not, give the tree a couple of spring weeks to see if new
buds form anywhere.
Bear in mind that if the buds form below any graft union (look for a
lump or scar low down on the stem), the branches that grow will be of
the rootstock and not the tree you envision. If that's the case, the
root stock is alive but probably not what you want for your orchard or
landscape and you can move the tree to some wilder location.
Meanwhile, as the spring comes on you should examine the cherry
carefully to see if it died from any disease (look for dark,
discolored tissue) or from insect damage (look for peeling bark or
tunnels under dead bark or tissue - if it's fully dead, check the
roots and planting hole when you excavate it to see if the roots were
eaten or perhaps rotted from the planting hole holding too much water
in all this rain.