I work at what's known as the body-building gym of my town. Wherever you have heavy lifters, you have people with shoulder injuries, and thus there are the few of those trying to do what they can to take care of their shoulder health. There's a lot of common error when I look at lifters getting their shoulders warmed up, though, so here I am science-ing them to correction.
Firstly, let's talk about the rotator cuff. These four muscles are constantly being bogged down by injury, whether it's tendinosis, muscle tears, or impingement. The first error I run into are the people who think that simply keeping your rotators strong is the key to good shoulder health. However, most of the time when we have chronic shoulder injuries, it is not usually due to the rotator cuff being weak. In fact, even if the rotator cuff has an overuse injury itself, it is almost always as a result of weakness elsewhere around the shoulder girdle which is forcing the rotator muscles to overcompensate or causing other structures to restrict it. Most of the time, shoulder rehab programs are going to require more scapular strengthening, using muscles such as the serratus anterior in order to stabilize the shoulder blade and relieve the workload of the rotators. Here's one fairly basic warm-up exercise you can use to hit the proper muscle groups.
For something a bit more complex as you get stronger, I'll refer to one of the most well-known "shoulder guys", Eric Cressey.
So now that we've determined that you do still get to do rotator exercises, how do we do them? Firstly, here's what not to do. The most common incorrect method I see is the standing dumbbell variation...
So wrong that it hurts. Probably her more than me though.
The problem here is that if you think about the angle of gravity with this exercise, this doesn't hit your rotators at all. With the downward pull at your shoulder from gravity, the only muscles that are actually working are your deltoids and traps. A line of pull to give resistance to the rotational movement is absent. If you're going to use dumbbells to hit the correct muscle group, you're going to have to lay down on a bench, first on your back and then on your side to hit the internal and external rotators, respectively. Standing with your arms at 90 degrees for external rotation works as well, but you'll still need to reposition to the bench for the internals.
The easier solution for your exercise is to use either a band or cable with a horizontal line of pull. I'll make one tweak to usual way of doing it, however. While performing your internal and external rotation, squeeze a towel between your elbow and body. The first reason for this is that it puts your shoulder girdle into "scapular plane", which is essentially the angle that will be the most stable and ideal for the shoulder to be moving in. Secondly, having the towel to hold on to ensures that you don't make the common cheat and allow the arm to lift away from the body, again creating compensation using your delts.
To conclude, if you want to keep your shoulders strong and stable in the gym, exercise the rotators using a band and don't neglect your scapular muscles in your upper back. Yes, we all want to get over to the bench press as quickly as possible, but proper prep before your workout will save you more time out of the rehab clinic later.