Exercises without weights are called bodyweight exercises, because obviously they are just using your body and gravity. When you lift a part of your body up, one or more muscles have to do work. All muscles are designed to lift certain parts of the body. With bodyweight exercises you increase the weight by getting the muscles to lift more of the body, up to a maximum of the entire body weight. Bodyweight exercises are very common. Press-ups, sit-ups and pull-ups are all examples of simple bodyweight exercises.
All exercises can be adjusted to make them slightly more difficult or slightly less difficult. To begin with, making an exercise more difficult usually means making that muscle move more weight. Making a muscle move less weight makes the exercise easier. You 'can' do this by adding or removing weights but you can also do this by simply adjusting your body position, which is much cheaper since you don't have to buy weights or pay for a gym membership, but you do have to think a bit.
There are several principles involved in adjusting the difficulty of exercises. To understand these you must first understand how muscles work. The muscles that control a particular joint are usually located on the side of the joint that is highest when standing straight. There are always at least two muscles working on each joint to allow for movement in both directions. Muscles can only pull, never push. One muscle pulls on the bone to bend the joint in a certain direction. Another muscle pulls on the same bone in the opposite direction to bend the joint in the opposite direction. At some joints there are more than two muscles involved in producing the range of movement but each muscle can only pull the bone it is attached to towards itself. You need to bear this in mind when choosing which exercise to use to exercise a muscle.
All joints divide the body into two parts. The parts connected to the bone above the joint and the parts connected below it. When a muscle pulls across a joint it will use the one part as an anchor from which to move the other part. Normally it will be the heaviest part that remains still, but if you anchor the lighter part then the muscle is forced to move the heavy part when it contracts. You can easily observe this, by lifting your arms up and down, and then keeping hold of a bar above your head and trying to repeat the same body movement. The further away from the centre of your body the joint is, the bigger the difference in weight between the two parts. This is the most fundamental way of increasing the intensity of an exercise.
The portion of body weight that a muscle moves in an exercise can also be adjusted by changing the level of support the muscle is getting. This is a fairly simple process of making sure some of the weight of the body is supported somehow, either by resting on or leaning another part of the body against an object. Leaning against an object obviously provides less support than resting on an object, since it is only an indirect support. To demonstrate this, if you try and do a press-up without the support from your feet touching the floor you will find that it is much harder because your muscles have to support much more weight. Also, the lower the support in relation to the rest of your body the more support it can provide. If you try and do a press-up while your feet are resting on the seat of a high chair you will again notice how much more difficult it becomes.
All joints act like levers and the same principles apply to joints as to all levers. The further away from the pivot point a given weight is, the harder it is to move it. Again you can test this easily by holding a heavy bag in one hand, first against your chest with elbow bent, and then out at arms length. You will notice that it much more difficult to hold the bag when it is further away from your shoulder. This principle also applies to supports. Supports further away from the heaviest part of the body or further away from the muscle being worked will provide less support than supports close to it. Doing a press-up with your knees touching the floor feels easier than one where it is your toes touching the floor.
These principles take a bit of getting used to but they mean that bodyweight exercises can be just as effective as weight training, especially when combined with plyometric principles.