I find tight shoulders on guys who do heavy lifting and people who have just started exercising. It makes for a very difficult downward facing dog. If you have tight shoulders you would find yourself not able to extend into a full down dog but instead fall somewhere in between a down dog and a plank. Your weight ends up more in your wrists and arms and it can get uncomfortable.
For many people simple alignment can remedy this. Make sure you come into a perfect -shoulders above the wrists plank pose first. Your butt should be in line with your entire body. This is your hand and foot position for face down dog -so keep hands and feet where they are. Now lift the hips for your down dog. Press the hands into the mat full, wide fingers -middle finger facing straight ahead. Reach the chest towards your thighs and keep hips high. You should be able to straighten out your arms and feel your upper arms externally rotate outward. Eyes of the elblows move forward, unless you tend towards hyper extending elbows like mine. (If you tend to hyper extend give yourself a micro bend in the arm, it shouldn't look noticeably bend.) Heels will reach downward but don't compromise having high hips in order to pull your heels downward. Also don't compromise having your hips high in order to straighten your legs. Hips high is more important. You can bend your knees a bit til you become more flexible. So one key point here when I spend bend your elbows and/or knees a bit if this applies to you....really its only just a bit! Micro bends!
Sometimes a simple physical adjustment can help. Come slightly forward on your down dog...now externally rotate your upper arms, then push back to downward facing dog. Here is where as a teacher I would simple press on the small of the back. Just on the sacrum area. Press slightly forward and then encourage the rest of the spine to shoot straight downwards toward the shoulders and arms. Sometimes physically helping the person to open up in the shoulder blades and relax the shoulders and upper back could help as well.
Now for those who are really really too tight. Let's take your down dog to the wall. Stand in front of the wall arms extended forward. Place your hands shoulder height, press palms into the wall as if was the floor. Take 1 or 2 steps backward, pull your hips back, press into your hands, drop the head and neck down. Really release your shoulder muscles here. This is great for beginners because maybe your shoulders are too tight and holding downward dog might be too much on your arm muscles and wrists. This is difficult because down dog should feel somewhat comfortable. I think of it as home base in my Vinyasa practice. Practicing this against the wall takes the pressure off your arms and allows your shoulders to still benefit from the pose! As you try to go deeper you can walk your hands slightly lower on the wall and feet a step or two further back.