Hatha Yoga
Hatha Yoga is the path of Physical Yoga or Yoga of Postures is the most popular branch of Yoga. Hatha Yoga considers the body as the vehicle for the soul. It uses physical poses (Asana), breathing techniques (Pranayama) and Meditation in order to bring the body into perfect health and for the more subtle spiritual elements of the mind to emerge freely. The practice of Hatha Yoga will result to the union of the body and the soul. It aims to make the body perfect and fill it with life force.
Bhakti Yoga
Bhakti Yoga is the path of heart and devotion or the Yoga of devotion. Yogis who practice Bhakti Yoga sees the Divine in everyone and everything they encounter. This lead the practitioner to develop love, acceptance and tolerance for all. Bhaki Yoga teaches a person to have a devotion to God and all things through devotion to life and love.
Raja Yoga
Raja means "royal". Raja Yoga is the path of Yoga that focuses on meditation and contemplation. It is based on the Eight Limbs of Yoga which is discussed in the Yoga Sutra. This Yoga path teaches deep self respect through self mastery. The self here is honored. Raja Yoga believes that the universe exists for the self, giving the self an illusion of centrality which results in self respect and respect for all creatures. Raja Yoga is also referred to as the King of Yogas and the majority of its practitioners live in spiritual or religious orders.
Jnana Yoga
Jnana Yoga is the path of Yoga that deals with wisdom and knowledge or the Yoga of the mind. Jnana Yogis pays tribute on man's intelligence. It tries to surpass limitations by unifying intellect and wisdom. Jnana Yoga tries to obtain existence beyond doctrine and ideological controversies by accepting all other philosophies and religion. It also uses an open, rational and curious mind in studying the spirit.
Karma Yoga
Karma Yoga believes that your present situation is based on your past actions. Karma Yoga is the path of service; it refers to the energy of action. This path requires you to be selfless. Performing a selfless service is the essence of Karma Yoga or consciously choosing a future that is free from negativity and selfishness knowing that your life is a consequence of your past actions.
Karma Yoga practices try to change your action towards the good - good words, good thoughts, good deeds, in order to change your soul. By being selfless, you change your consciousness which leads to a change in your destiny.
Tantra Yoga
Tantra Yoga is the path of ritual and perhaps the most misunderstood path. Some may think of Tantra Yoga as sorcery, witchcraft, magic spells or some mysterious formula. Most people perceive Tantra Yoga as sexual. All of these perceptions are far from the truth.
Tantra is the knowledge concerning Tattva (Truth or Brahman) and Mantra (mystic syllables). It utilizes rituals to respectfully experience the sacred in everything we do, not just sex - though sex is a part of it. It aims to expand our awareness in all states - whether awake or asleep. Tantra Yoga practitioners must have purity, humility, devotion, courage, dedication to his Guru, cosmic love, faithfulness, contentment, dispassion, non-covetousness, and truthfulness.
I hope this helps to make it all a bit clearer!