Many medicines must be injected "subcutaneously" (SQ), which means beneath the skin (and NOT into any of the underlying tissue or muscle). You'll notice that this doe is bouncing around quite a bit, but is securely fastened in the milk stand. Start by grabbing a loose bit of skin on the neck and lifting to make a "tent" with an empty space underneath. Wiggle around a little bit to make sure that the tent is nice and loose from the surrounding area. Stab the needle through the skin into the tent. The tip of the needle should end up in the center of the tent. Wiggle the syringe around a bit to make sure that the tip of the needle hasn't snagged something. You don't want to deposit the medicine into any other place than the open area. (Some medicines can cause fatal results if injected into a muscle or blood vessel.) Firmly pull back on the plunger to make sure that you haven't contacted a blood vessel. You should see a empty gap at the base of the plunger. Then release the plunger and slowly inject the medicine into the tent. Look to make sure the needle hasn't gone all the way through, in which case the medicine will come out the other side and start dripping down the neck. If the flow slows down, stop to see what is wrong; don't force it. Wait a moment so that you aren't injecting fluid as the needle backs out through the skin. Now pull the needle out.
Whenever you give a shot, make sure to watch the animal for about an hour to be sure that it is not having an anaphylactic reaction (shortness of breath, foaming at the mouth, etc) in which case the only remedy is an epinephrine shot (which now can only be obtained from a veterinarian).
