Classic Hinduism promotes four different goals. Like other aspects of Hinduism, the goals are split between those emphasized by the "life is good" perspective and those emphasized by the "life is bad" perspective. The three life-affirming goals are Dharma (virtue), Artha (success) and Kama (pleasure), while the life-negating goal is that of moksha (release).
The three "life is good" goals can be pursued all at once or at different times in one's life. Some goals seem more suited to different stages of life than others.
Dharma is the practice of virtue, the living of an ethical and ritually correct life. The definition of what is virtuous, however, varies, depending on a person's caste and jati membership. The primary virtue is to fulfill the duties assigned to one's caste. Thus a brahmin should offer sacrifices and do them to the best of his ability, while a Vaishya silversmith should create his plates and bowls as strong and beautiful as possible. If either person tried to do the other's job, that would be seen as violating their caste duty. The dharma a person is expected to fulfill also varies depending on their stage of life. A student, for instance, becomes virtuous through a different set of actions than a householder.
Artha is the working for and achieving of success, in terms of both wealth and power. This means it is religiously important to be a successful businessman, to sell a lot of carpets for instance, or to manage a successful restaurant. It also means that it is religiously good to serve on the city council, to be active in civic organizations, or even to become a politician. This kind of success is most easily achieved at the householder stage of life.
Kama is pleasure, usually understood as aesthetic pleasure of all kinds. This includes: the producing and enjoyment of art, music, dance, drama, literature, poetry, and sex. (The "Kama Sutra," which may be one of the best known Hindu texts in the West, is about the aesthetic pleasure of men and women; it discusses beauty, music, dance and sexual activity.) It is thus religiously praiseworthy to take part, to support, or just to appreciate any form of pleasure. This should always be done, of course, within the realm of dharma (i.e., in a virtuous manner).
The "life is bad" goal is moksha. It is the striving for release from life (since, after all, it is bad). To achieve this, a person must turn their back on life and strive to live without the things that make up life. At first, it requires the turning away from the first three goals, of rejecting family, comforts, pleasure, education, and so on. It also requires one to become an ascetic, a hermit, and to spend one's time in contemplation. This contemplation should be directed towards overcoming the maya that clouds human perception of reality and towards realizing the true nature of the cosmos and one's place in it (that atman and Brahman are one). (For further discussion, see The Cosmos.)
In Hinduism, there are four main ways to reach towards the divine reality, whether the ultimate goal is a better life, union with the divine, or a release from life. The ways are called yoga, a word similar to the English term "yoke." And, just as yoke implies a burden or a discipline of actions, so too does yoga. Each yoga puts on its followers a set of actions that help lead the practitioner towards their goal. The yogas are: Jnana yoga, Bhakti yoga, Karma yoga, and Raja yoga. The first three are discussed in the Bhagavad Gita, while the fourth derives initially from the Yoga Sutra. These are all spiritual approaches to understanding the divine world; what we in the west generally term yoga--forms of physical exercise and control of the body--is properly known as Hatha yoga. It has no spiritual impact.
Janana means knowledge and this yoga is the path to understanding ultimate reality through knowledge. Of course, the reality the yogi (a practitioner of yoga) is trying to comprehend is the identity of atman (one's own soul) with Brahman (the creator and essence of the cosmos). And comprehension of this identity must happen not just at the intellectual level, but with every fiber of a person's being.
There are three main steps in Jnana yoga. The first is learning. The initiate is taught about the identity of atman and Brahman through instruction, study of holy writings, and so on. Once the intellectual understanding of the concept has been achieved, the yogi moves to the next level.
The second step is that of thinking. The yogi is taught to embody the teaching he has received. The teacher often encourages this process, for example, by pushing the student to think about the "I," "me," and "my" that always crop up in a person's speech. The goal of this stage is to bring the yogi to the ability to separate his/her eternal soul (the Self) from the temporary self within which it is encased.
The third step is to differentiate oneself from oneself. In other words, once it is understood that each individual's eternal atman is enclosed in a temporary body of maya, the goal is to relocate one's identity in the atman, rather than in the body and its temporary accompanying emotions and thoughts. In the initial stages of this process, the yogi begins to think of themselves in the third person. Rather than thinking, "I am taking a bath," they think, "John is taking a bath." A person thus becomes an observer of their temporary body, rather than its motivator. The ultimate aim is complete detachment of the eternal Self from the temporary one. Once this is achieved, then there is nothing that separates the Self (the atman) from Brahman.
This is the path of devotion to a god, or, more precisely, the path of the love of a god. A person thus centers on a god or goddess (such as Vishnu, Parvati, Ganesha) and expresses their love for him or her. The goal is not to just say "I love Shiva" or "I love Kali" or just to perform acts of love and worship, but to actually love them, to devote oneself to them as if they were a lover, a parent or one's child.
Bhakti takes many forms. It can be the constant repetition of the god's/goddess' name throughout the day to enhance a person's awareness of the divine being's role in life. It can be the giving of gifts to the god at his temple, and the participation in worship of the god there. It can be pilgrimage to a site sacred to the goddess' life. The goal is thus not identity or unity, but nearness. Lovers are not one person, they are two people whose lives are intertwined. So too it is with the worshipper and their god.
This yoga aims to reverse the natural order workings of karma. Karma is generated by every action a person performs during their lives, and, it is the working out of karma that requires rebirth after death. So, Karma Yoga reasons, if a person could live without generating karma, then there would be nothing to cause rebirth.
This task is accomplished by detachment, namely, the detachment of one's Self (one's atman) from one's actions. This is done by removing all involvement, including one's intent, from their activity. This can be accomplished either through the knowledge of one's true Self (like Jnana yoga) or by putting all the actions onto one's god (following a path similar to Bhakti yoga).
Raja means "royal," so this is the royal yoga. This is essentially the path of meditation, that is, of being able to remove one's own consciousness from its awareness of this world of maya and to focus only on the ultimate reality of the cosmos' unity. This is quite difficult to accomplish, and there are eight stages that are designed as the simplest path. The difficulty is to overcome one's awareness first of their surroundings, and then of their own body and its activities (such as breathing and the pumping of the heart). Once this is accomplished then a person must take control of their mind and to focus it on one thing only, Brahman. The goal is achieved when through concentration and meditation, all separateness of the world of maya disappears and the unity of atman and Brahman appears.
Note: In the preceding discussion of yoga, I have drawn heavily from Huston Smith's discussion in his The World's Religions, pp. 26-50.