When something gets close, the bow arm comes up - no tension on the string. As the critter moves toward ya, slowly and smoothly shift so the bow is always facing them. As they walk by (or duck their head, look the other way, pass behind a tree) you quickly but quietly come to full draw and fire.
This is of course the hardest part about hunting with this equipment, because unlike modern hunters this whole sequence happens at under 20 yds. There are myriad tricks to pulling this off, but none of them make it easy and you will fail more often than not. But then, if it were easy, anyone could do it..