I suppose it would depend on the tribe? On the Redhawk Outdoors television show they say a prayer in their native language and blow in each of the deer's nostrals.
Ted Nugent spoke of his first buffalo hunt with native americans, he said they prayed and burnt sweet grass. I've also heard of them burning sage.
Thomas Stetson wrote a book and somewhere in it he talked about hanging the deer's pelvic bone from a tree and putting red ribbons on it.

"Hey ya'll, watch this"