Chakra is the moulding of the physical energy. It is present in every cell of the body and the spiritual energy gained from exercise and experience. Once moulded, it can be channelled through the chakra circulatory system, which is to chakra as the regular circulatory system is to blood, to any of the 361 chakra points (called tenketsu) in the body. Through various methods, the most common of which is hand seals, the chakra can then be manipulated to create an effect that would not be possible otherwise, such as walking on water, exhaling fire or creating illusions.
By forms of chakra I assume you mean the shape, chakra control and the different types of chakra?
If so by you manipulating your chakra, you can shape it into different shapes. We've seen in the manga how Sasuke is able to manipulate his lightning and shape into a long blade. Chakra control is what requires you to stay concentrated on your technique, to basically make it happen. For example, there's a few techniques that require you to keep sending chakra, like golem technique. To be able to use it you need to keep your chakra control to direct it. and the different types of chakras, like elemental, raw etc. You can combine elemental chakras to create different types of abilities, like wind and water create Ice, fire and wind create scorch (If I remember correctly).
Hand seals are mostly used for a lot of ninjutsu and genjutsu techniques. The chakra is manipulated through hand seals, if said techniques does require any. Not all techniques require hand seals but the ones that do, require different numbers of hand seals. Also a lot of techniques are known by the hand seals, for example, the fireball jutsu is famous and is known to be performed by the use of the Tiger hand seal. Obviously Taijutsu doesn't require hand seals and Kenjutsu if I remember correctly.