Lust Rituals are conducted for the purpose of sexually attracting a person of your choice. You must have a particular person, or at least type of person, in mind for this to have any chance of success.
Compassion Rituals are performed for the gain of those you care for, or on one's own behalf. The purpose is to increase worldly gain for the target, whether it be a friend or yourself. Any ritual aimed at gaining material wealth, physical advantage, or increase in life station falls into this category.
Destruction Rituals are otherwise known as curses or hexes, and are employed for the destruction of one's enemies.
WARNING: in each of these cases, the only risk is that you must truly want to see what you have wished for come to pass. It very clearly states that there is no guilt-ridden risk that your rituals (specifically, destruction rituals) will be returned upon you (such as the "threefold rule"), but rather that you must be aware of the consequences should you get what you want. He advises that if you perform a lust ritual, that you be prepared to take what you have desired should it come to you; if you perform a compassion ritual, be aware that all gains may be at another's expense; if you perform a destruction ritual, that you should not care whether your enemy lives or dies.