A good 10-minute warm-up won't just keep you pain-free and increase your longevity in the gym, it'll also boost your strength and muscular gains. A quick (but effective) warm-up has three components. Let's break them down.
First, get some blood flowing. Spend 3-5 minutes doing some form of general "cardio." The general warm-up increases your core temperature and loosens up the muscles you're about to hit.
You could just jog for a few minutes, but there are better and less boring low-impact alternatives like sled pushes/drags, the rowing ergometer, or the VersaClimber. All will help to drive blood flow to the hips and upper back which will lead to a more effective workout.
Now do 2-4 minutes of "muscle activation." Pay special attention to your vulnerable areas such as the shoulders, knees, and lower back. Below are some good exercises that'll put you in good alignment before lifting. Do 1-2 sets.
Horizontal Band Pull-Apart
Vertical Band Pull-Apart
Doing these with the palms over and under will allow for more mobility throughout the shoulder. Keep your ribcage down and core engaged.
Banded Side Step/Banded Squat
Drive your knees out against the band to activate the glutes.
This will help protect your lower back by teaching you how to brace your core as you resist rotation.
Now spend 2-4 minutes going through a series of active dynamic stretches. To make these efficient, perform movements that engage the most amount of musculature possible. My favorite is "the world's greatest stretch" but I add two components that make it better.
World's Greatest Stretch (Made Better)
Begin by taking a big step forward with your right leg and lower your body into a lunge position. As you lower your upper body, keep your left hand on the ground for balance and reach your right elbow to the inside of your right foot. Next reach your right arm up towards the ceiling and twist your body towards your right leg.
Here's where we improve upon the stretch…
Once you have fully twisted towards the right leg, rotate your pinky down towards the ground (externally rotate the humerus) and reach your bicep behind your ear. This will allow you to get a deep stretch through your lats.
Now grab your toes with your right hand and pull them up as you press your heel into the ground and gently extend your knee. This will stretch your hamstrings throughout a full range of motion, prepping them for your training session.