Peter Carroll first described the eight forms of magick in Chaos Magick in his book Liber Kaos. Each of the eight forms have been assigned colours which have an emotional significance to the assigned ray on the chaostar.
Octarine - Pure Magick
Octarine is a term created by Terry Pratchett for his Discworld books. Octarine is the eighth colour of the spectrum on the Discworld and represents magick.
It's colour is different for any mage, depending on his personal perception.
Octarine stands for the mages instinctual drive to magick, through it we are able to create our mage-self. Workings with gods of magick are also cast in octarine light, such as Freyja or Odin.
This form of magick is also for the development of theories or philosophies, for creating an Alphabet of Desire or a new divinatory system, developing a magickal language and similar purposes.
Lastly octarine workings are an inspiration to the magician.
Black - Death Magick
This form primarily deals with spells of destruction, but also with spells of avoidance of death such as rituals of evocation of the death self. The purpose of such rituals is to come with terms with aging, morbidity, entropy and decay as well as for the experience of feeling Death approach which can be used for help in changing belief systems.
The purpose of rituals of destruction is to send an encoded message into the target with the ultimate goal of promoting self-destruction in the victim. This usually happens in cold blood, while in War Magick (Red) it happens in hot fury.
Blue - Wealth Magick
Wealth can be measured by material wealth and the influence one has over others. Obviously the purpose of this branch of magick is to multiply wealth, which is only possible by constant input and output.
Use blue magick to develop a consciousness for money. Establish good terms with the concept of money, get a taste for it, get to know what it likes and what not. Wealth means movement, to horde it is to lose it.
Wealth magick can also be used to exorcise any negative feelings towards wealth.
Green - Love Magick
This form deals with relationships of all kind, be it friendships or actual love. The Green focuses on the art of making friends, creating loyalty and affection.
Green magick can be used to like yourself more, create and promote loyalty, prevent mobbing etc. Green workings start best with an excessive act of self-love, to see how gorgeous the own body is as well as the personality.
It can also be used to enhance your empathy. Behaviorial matching however as heralded by many self-helpers are dead out, most people just feel mocked if they are copied. The key here would be similarity, not a 1:1 copy.
Yellow - Ego Magick
Frequently refered to as "solar magick". In Ego Magick the magician works with himself. It involves rituals and workings to change the ego, works of illumination.
Paradigm shifts, deleting and creating new beliefs, the LHP concept of coming into being - "Xeper" - falls in this form of magick.
Purple/Silver - Sex Magick
In Sex magick, any form of sex is used to reach gnosis, be it auto-erotic or with a partner or partners.
This form of magick can be used to create tremendous inspiration in all areas, as well as to come to terms with sexuality and removing abnormalities.
Another use is to project sexual glamour to attract others for the sole purpose of getting laid. There it must be said though that it is far easier to cast for a suitable partner in general that you can live with instead of trying to enchant a specific person.
Orange - Thinking Magick
Mercurial magick falls in this category. Hermes/Mercury can be considered the patron of this form of magick. It involves trickery, charlatanry, living by wits alone and thinking fast.
It's driving emotion is fear, fear can both accelerate thinking as well as slow it. The Orange can be used to enhance luck or help in crimes or studies.
As Hermes was also the messenger of the gods, orange magick can also be used for workings of communication.
Red - War Magick
Conflict, the prime force that drives evolution ever forward. Without the red, humanity wouldn't have survived. Without it few discoveries would have been made as most inventions and studies were done in order to get an advantage over the rest of the world.
War magick can be used to promote vitality and aggression to help in conflict situations and to perform war spells. The goal can range from intimidation or control to killing the victim.