Before intense exercise it is important to warm up beforehand with a low-impact activity to improve circulation and to warm down at the end with more low-impact activity. The body cannot cope well with sudden changes in the level of activity and warming up and cooling down will soften the process, help the body adjust and help avoid injury.
When exercising you should consider the body as a whole and look to improve all areas. The most important thing to remember while exercising, or training in general, is to listen to your own body. Your body will give you signals when it is time to stop, whether it be pain, fatigue or whatever. Exercising should not be rushed and as long as you and your muscles are tired at the end of a training session then you are pushing your boundaries and improving. When you are experimenting and learning how to exercise your body, if you go slowly you can listen to the signals your body is giving you and use them to judge whether or not to continue. If you try to go fast and do a lot of intense exercises then if an injury happens it will also happen very quickly and that will make it harder to avoid.
For example, if you do a lot of leg exercises in one session then at some point your legs will start to feel tired. You then judge how tired your legs are, for example on a scale of 1 to 10, with 1 being completely fresh and 10 being unable to move, and compare that to how strenuous you want this training session to be. The more strenuous a session the better the exercise, as a general rule, but remember that you will need longer to recover from more strenuous exercises. Also bear in mind that there are other things apart from training that you might need your muscles for. It is not a good idea to exhaust yourself completely on one day if you need to be active the next day.
As a general rule, your muscles need time to recover completely from a training session. This doesn't mean you can't train every day, but try to exercise muscles that aren't tired. The rate of recovery varies from person to person (and it is something you can train your body to improve by gradually reducing the time between sessions), but it is generally between 1 and 4 days, depending also on the intensity of the exercise and other factors such as diet and degree of rest.
Exercises need to be challenging but not impossible. You should be able to do it but then feel tired at the end. Once you begin to understand how exercises work you will find it very easy to adjust them to suit your needs, so that they are neither too easy nor too hard. The way you judge whether they are too easy or too hard is based on how many times you can repeat it and whether you want to improve strength or stamina. If you want to improve strength and power (push harder, lift heavier) then you should find exercises that you can repeat only a few (3-5) times before you start having real difficulty in completing the exercise again. If you want to improve stamina then you should find exercises that you can repeat around 30 to 40 times. It doesn't matter too much if you can do slightly more or slightly less, so if you're aiming for 10 and do 12 that's not a big problem, but that's about the number you're looking for. If you are consistently able to do many more repetitions than your target, or many fewer, then you should think about adjusting your exercise or finding another exercise completely.
With a bit of research and experimentation you can find many individual exercises and types of exercises that you can use to exercise in a way that suits your body and situation.