Moves Explanation

Jumping jacks
Jump up and push your legs apart, at the same time move your arms sideways above your head and clap them together. With the next jump you lower your arms back to your side and pull your legs together.
Mountain climbers
Place yourself on the floor on your hands and feet, almost like a planck position just on your hands. Jump your feet alternating forward towards your hands. Each jump is a count.
Lunges
Starting position is normal standing again. Pull your arms straight above your head. Step with one leg forward in a big step (your both knees are bent, however watch out that your knees are in a straight line with your ankles). Now move vertically downward until the knee behind you is touching the ground. Then push yourself back to a standing position, using the forward leg. This was one repetition. Do the lunges alternating.
Frog
Starting position is again standing position, your feet shoulderwide (look in the mirror - ankles of your feet below your shoulders, toes can point outwards). Fold your hands together in front of you. Bend forward and place your elbows between your legs (knees). Look straight forward. Move your hips slowly downwards so you reach the 90 degree angle, and slowly upwards.
Burpees
Stand like you would like to do a squat. With your hands go down to the floor in front of your body, touch the ground. Jump your feet backwards like in a planck position. Lower your body to the floor and push yourself back up again. While you push back up, jump your feet forward again, raise your body upwards, raise your arms upwards at the same time, and jump, clapping your hands above your head once. When you land on the floor with your both feet standing, you have fulfilled one Burpee.
Air squats
Starting position is standing position, your feet shoulderwide (look in the mirror - ankles of your feet below your shoulders, toes can point outwards). Raise your arms above you, move your hips backwards, and bend your knees. The knees should move to the outside if you want to avoid any kneecap insuries. Knees should not move forward over or past your toes. Bend your knees and hip enough to reach at least a 90° angle or even less. Raise back upwards, lowering your arms back to a standard standing position.
If you are not sure of your posture there is an easy way to find out. Place yourself in front of a wall or mirror (stomach towards the wall, feet none to very short distance away from the wall). Raise your arms above your head and touch with your palms the wall. Look straight forward. Now, move your hip backwards and lock the hips, your upper body will have to keep straight. Slowly start flexing your knees. If your knees are touching the wall, you push your knees in front of your toes, which will hurt your knees in the longrun. So in order to do a propper squat, move the knees to the outside and watch out they are not moving in front of your toes.. If that requires you to point your toes further outside, please do so. Now bend your knees further until you reached a 90 degree angle and if possible even lower. Yes you read correctly, you can break the 90° angle. Its incorrect if people tell you a squat is bad for you or it should not break the 90° angle.
If you do not know when your 90 degree angle is arrived, you either can place your suitcase or a chair behind you (Note: the height should be below your knee folt).
Test this at least 10 times until you have the feeling for the correct posture during a squat.
When doing the exercise itself, you start out with a standing position, heels shoulderwide apart, toes slightly pointed outside, arms hanging down, straight back. Move first the hips, then bend the knees; at the same time move your arms forward. This will ensure you keep your upper body straight.
If you are very experienced and your own bodyweight is not enough anymore, raise your suite case, laptop, a hotel room chair above your head doing the whole exercise. This is generally called an overhead squat.
Competition sit-up
Sit on the floor, feet flat on the floor, knees bend and pointing upwards. Move your knees to the side so the buttom of your feet is moving off the ground pointing against each other. Now raise your hands above you and move backwards until your upper body lays on the floor with the back. Move back up, trying to leave your feet on the floor. Move forward enough so you can reach and touch the ground in front of your feet. That was one repetition.
Side to side
Sit on the ground with your legs extended, torso straight up. your both hands are grapped together like you are holding something. Move your upper body backwards, until you have reached an approximately 45° angle between the torso and the ground. Lift your legs straight up, bend the knees slightly. The only touchpoint to the ground will be your buttocks, you balance your body on it. Start moving your hands from side to side but twisting your upper body left and right. The hands should touch the ground with each twist. Each side touch counts as one repetition. To make this exercise more challenging, hold an object between your hands like a water bottle or the iron of the hotel room (just avoid hammering the object on the ground).
Planck position
For the planck position lay on the ground on your stomach, legs extended. Lean your torso on your elbows and your legs on your toes. Your trunck is off the ground, forming with the shoulders and the legs a straight line. This move includes no movement of any bodypart, the exercise is to hold the position as described.
Push-ups
Keep a straight line between your head and your feet (or for beginners between your head and knees), tighten your stomach muscles to keep your torso in place. The fingers of your hands should be spread, arms shoulder-wide apart from each other. When you lower your body, your elbows move to the sides of the torso. You should lower your body so far, that your chest is almost touching the floor, means your upper arms and your back have to be even. Look straight to the floor, not down on your body, or look ahead of you on the foor.

Leg Lift

Lay on the ground on your back, legs extended. Place your hands below your lower part of the buttocks for support. Move your both legs upwards together until they are fully vertically extended to the ground. Lower the legs again. That is one repetition. To make this more difficult, place your hands not below your buttocks. You will see right away a difference. To make it even more challenging, hold an object between your legs. 

Stretching

1. Static stretching
2. Active stretching
3. Dynamic stretching
4. PNF stretching

1. Static stretch means holding a muscle group stretched for about 30 seconds, repeat this 4 times. This is best used as post-workout. Static stretching is helping to improve your flexibility in the long run.
2. Active stretch means to hold the muscle group that needs to be stretched with the opposite muscle. If you try out this stretch, you will notice that you won't be able to hold it longer than 10 seconds.
3. A dynamic stretch is pretty much described in its name. You are keeping your muscles moving/dynamic. This kind of stretch is doing barely anything for your flexibility but I strongly suggest to implement the dynamic stretch into your warm-up. Trust me its a good thing to do. I should have done that last weekend as I normally do.
4. Last but not least there is the PNF stretch (Proprioceptive Neuromuscular Facilitation Stretch), which provides you as well with an improvement of flexibility in the long run. The PNF stretch is often done with a partner, but you can also use a rubber band or tower. An example how to do the PNF stretch of e.g. the hamstrings (muscle group on the backside of your upper leg): lay on the ground, lift one leg vertically up, keep the other straight on the ground. Take a towel and hold your leg vertically upright (don't bend) with a slight stretch in the back of your leg - only a slight discomfort should be felt on the hamstrings. Then contract the hamstrings isometrically for up to 5 seconds (means don't move, just contract the muscle without changing its length of the muscle). After releasing the contraction, use the quadriceps (front muscle group of your upper leg) to further move the leg toward your torso until the discomfort is felt again. Hold the position with your towel and contract the hamstrings isometrically. Repeat this procedure another 2 times.
So to summarize: Use the dynamic stretch for your warmup, and use the static stretch or PNF stretch for your post workout. Keep breathing throughout the stretches, all together is will also relax you.
So what did I do today? I used mainly the dynamic and PNF stretch for my legs, static stretch for my shoulders and torso. I needed about 30mins for everything.