It is very important for all tennis players to keep their limbs warm and ready to play at all times, doing this helps prevent injuries. Here is a list of helpful warmups and stretches to do before or while playing tennis:
Fish stretch:
Clasp your hands behind your back, palms facing outwards.
Bend forwards, your torso should be close to being parallel to the ground, and your arms almost vertical
Do this stretch slowly and gently, it is completely fine if you cannot do this stretch the whole way
Across the body shoulder stretch:
Pull your right arm across your body with your left arm, keep your right arm straight, but bend your left.
Hold for 15 seconds and switch sides.
You should feel this stretch in your shoulder.
Standing quad stretch:
Stand straight with your feet a shoulder length apart.
Slightly bend your right leg and lift your right heel.
Grab your right heel with your right hand, bending your leg completely.
Extend your left arm, leaning forward.
Hold for 30 seconds and switch sides
You should feel this stretch in you quadriceps.
Sitting hamstring stretch:
Sit on the ground, with your left leg extended, your right leg should be bent, with its foot touching your left thigh.
Lean forward, bending at the waist.
Extend your arms, and try your best to touch your left foot.
Hold this position for 15 - 20 seconds and switch sides.
You should feel this stretch in your hamstring.
Knee lifts: You can do this warmup in place or around a tennis court, put your arms to around hip level and raise one knee at a time to meet them. If you are doing this in place, do this for around 15 - 20 seconds 3 times. If you are at a tennis court, do this for 1 - 2 laps.
Butt kicks: Like knee lifts, you can do this warmup in place or around a tennis court. Raise one heel at a time (keeping your knees pointed down) to hit your butt. Do this for around 15 - 20 seconds if you are staying in place or 1 -2 laps if you are going around a tennis court.
Jumping jacks: Stand in place, with your feet together and your arms at your sides. Jump up, and split your legs apart while also lifting your arms above your head and clapping your hands together. Do around 4 sets of 20.
Jump Rope: Holding the jump rope at a 45 degree angle away from your body, stand with your feet together. Use your hands and wrist to swing the rope over your head - try your best not to move your arms as much. Right before the rope reaches your ankles, push off of the ground, and jump up about half an inch. Set a reasonable pace for yourself, and try to get bout 50 reps or more.