If you can see a deer's eye, the deer can see you -- and that's an important tip to remember. When a deer is close, don't move if it can see you. It's the movement that attracts a deer's attention. Unfortunately, you have to move in order to draw a bow or swing a gun.
Wait until the deer turns its head so you can't see its eye, or wait until it walks behind a tree or brush. If the deer steps behind some cover, there's a timing issue involved in getting the shot, because you can't hold a hunting bow at full draw for very long.
If the deer stops behind cover and just stands there, you might have to let down the bow and wait for an opportunity to draw again. Along with stand placement that puts you in position to get the shot in the first place, knowing when to take the shot is a critical aspect of bowhunting. The deer has to be close before you draw the bow, and any sound or movement can give you away.
The ideal situation is for the deer to be moving steadily along a defined trail. The best time to draw or aim is when he walks behind a bush or tree. When he steps into an opening, you should grunt to make him stop, then take the shot. It's hard to beat a broadside shot at a buck, so try to set up your bow stand at a 90-degree angle and 20 yards from a game trail. If the deer's walking the trail, you'll have a good chance at a broadside shot.