As for a stretching routine. A short cardio such as jumping jacks or jumping rope to warm up the muscles.
Here are a few that may not be well known:
I stretch my lower back by lying down face up. Bring the right knee up to the chest slowly and have my right arm under the knee as I slowly lift my head up toward the knee. Hold for 5 secs. Go back down and rest. Do the same motion then hold for 10 secs. Repeat until I can hold for 30 seconds comfortably. Now do the same motion except use the left arm under the right knee as you go through the motions again. Then change sides and repeat the whole thing for the left knee. The ground under you should feel flatter like more of your mass is making contact on the ground.
The Butt Stretch. Since your still lying on the ground cross your right ankle over your left knee (makes a figure 4). Now raise your left knee toward your chest. Brace both hands under the left knee. You should feel the stretch on the right glut muscle (right butt cheek). Hang out for 30 seconds to 2 minutes and breathe. Now switch with the left ankle over the right knee and repeat.
Speaking of butt, place your butt against the wall while you are still lying down on your back. You should be facing the ceiling, lying on your back, and your butt against the wall. Open your legs as wide as you can, but maintain contact with your butt against the wall. Make sure your knees do not roll toward the ground or the ceiling. Breathe and relax. This will help with the splits. After 20 secs see if you can go further. Keep this up for two minutes. Slowly. Slowly. Very slowly pull your legs in together.
TKD is the only art I'm aware of where we stretch for a cool down. I also recommend stretches after getting a massage (drink lots of water) if you want the work done on you to hold longer.