The Arya Samaj is a socio-cultural organization founded by Swami Dayanand Saraswati in 1875. The mission of the Samaj is to mould the lives of its members and all others according to the message of the Vedas with reference to the circumstances of the time and place. The Vedas are the poetry of eternity in meta language. They are pure knowledge, primary, original, universal, complete, revealed at the dawn of creation for all mankind without distinction or discrimination of race or colour, caste or creed or sex. The idea behind this universality is: God is one, His creation is one, his law is one, Humanity is one, Revelation is one; all that follows is historical and relative justifiable as corrective with reference back to the universal.

The Arya Samaj is a voluntary organisation working throughout the world for physical, moral, spiritual and professional education, eradication of superstition, inculcation of universal values, comparative study of cultures, religious and social systems, with open enquiry and debate for the propagation of truth. The organisation is thoroughly democratic and works on the basis of the ten principles formulated by the founder. The principles are universal and have no tinge of sectarianism at all

Arya Samaj in Hindu Dharma

The Arya Samaj , as founded by Swami Dayanand Saraswati, continues to be a reformist movement in India and within Hindu-Dharma worldwide. It is NOT a separate religion nor is it a sect within Hindu-Dharma. Its primary task is to reform Hindu-Dharma, which had been corrupted by 500 years of Mughal and 200 years of British rule. According to Arya Samaj, worship of God consists in 3 acts : 

(a) the first and foremost to study the Vedas, with the motivation to acquire knowledge of God.
(b) the observance of Dharma (moral duty and action) as prescribed by God in the Vedas.
(c) worship of God by fire or the homa-sacrifice, this involves the use of the Gayatri Mantra

The Vedas were created by God prior to the creation of the universe and given to the ancient rishis. It contains all the fixed truths of the universe, the True Knowledge. Such laws are unchangeable (i.e. Karma, Dharma and Physical laws), they are not of the changeable type (i.e. this webpage has the colour 'x'

The problem that arises is that Vedic Sanskrit is radically different from Classical and Epic Sanskrit, the result has been many misinterpretations by Western scholars. For example, "Ashva" means "horse" and "grain". Sacrifices which call for "Ashva" were assumed to be for horses but the correct Vedic interpretation is that of "grain". The point being is that Vedic Sanskrit must be read in respect to the Vedic context.

There are four other substantive claims that Swami Dayanand makes regarding the Vedas: 
(a) In the matter of religion and in the spirit, the Western mind has not reached either the depth or the heights commanded by the Ancient Indian mind.
(b) In the matter of the social, the Indian solution aimed at in ancient times are as good and sound and effective as those arrived at in the West in modern times. 
(c) In philosophy, India has nothing to learn form the West. 
(d) In physical sciences, the West is far in advance of the Ancient Indians. India has had its successes in this regard. In 500 B.C.E., the Indian surgeon Sustra performed cataract surgery for the first time in the civilized world.

Caveats & Clarifications

(a) The Arya Samaj does not believe in the infallibility or immunity from mistakes. To err is to be human.  
(b) The only appropriate forms of worship are that of the fire (havan).
(c) The Arya Samaj believes in the Law of Karma. This is the truth that "acts must follow by their consequences, that the result of actions cannot be warded off or atoned by any means". This is in connection with the theory of reincarnation.
(d) The Arya Samaj does not believe in "Fate". Those born in a lowly position are not condemned to live a life of despair. It is the soul system that has degraded people to punish them for the positions of the rich and powerful.
(e) Everyone can make and unmake his or her destiny through the Law of Karma.
(f) The Vedas are infallible and expects every woman and man to know them and to expound them for the benefits of others.