Raja Yoga is the method of attaining Realization through the control of the prana and psychic forces. The methods as outlined by Patanjali in his Yoga Aphorisms are for the most part accepted as the way to practice it in modern Vedanta. Swami Vivekananda says in the Preface to his book Raja Yoga (which includes his translation of Patanjali's Yoga Aphorisms), Complete Works, V1, pp 121-123, and available here under the heading Raja Yoga - http://cwsv.belurmath.org/volume_1/vol_1_frame.htm :
Since the dawn of history, various extraordinary phenomena have been recorded as happening amongst human beings. Witnesses are not wanting in modern times to attest to the fact of such events, even in societies living under the full blaze of modern science. The vast mass of such evidence is unreliable, as coming from ignorant, superstitious, or fraudulent persons. In many instances the so-called miracles are imitations. But what do they imitate? It is not the sign of a candid and scientific mind to throw overboard anything without proper investigation. Surface scientists, unable to explain the various extraordinary mental phenomena, strive to ignore their very existence. They are, therefore, more culpable than those who think that their prayers are answered by a being, or beings, above the clouds, or than those who believe that their petitions will make such beings change the course of the universe. The latter have the excuse of ignorance, or at least of a defective system of education, which has taught them dependence upon such beings, a dependence which has become a part of their degenerate nature. The former have no such excuse.
For thousands of years such phenomena have been studied, investigated, and generalised, the whole ground of the religious faculties of man has been analysed, and the practical result is the science of Râja-Yoga. Raja-Yoga does not, after the unpardonable manner of some modern scientists, deny the existence of facts which are difficult to explain; on the other hand, it gently yet in no uncertain terms tells the superstitious that miracles, and answers to prayers, and powers of faith, though true as facts, are not rendered comprehensible through the superstitious explanation of attributing them to the agency of a being, or beings, above the clouds. It declares that each man is only a conduit for the infinite ocean of knowledge and power that lies behind mankind. It teaches that desires and wants are in man, that the power of supply is also in man; and that wherever and whenever a desire, a want, a prayer has been fulfilled, it was out of this infinite magazine that the supply came, and not from any supernatural being. The idea of supernatural beings may rouse to a certain extent the power of action in man, but it also brings spiritual decay. It brings dependence; it brings fear; it brings superstition. It degenerates into a horrible belief in the natural weakness of man. There is no supernatural, says the Yogi, but there are in nature gross manifestations and subtle manifestations. The subtle are the causes, the gross the effects. The gross can be easily perceived by the senses; not so the subtle. The practice of Raja-Yoga will lead to the acquisition of the more subtle perceptions.
All the orthodox systems of Indian philosophy have one goal in view, the liberation of the soul through perfection. The method is by Yoga. The word Yoga covers an immense ground, but both the Sânkhya and the Vedanta Schools point to Yoga in some form or other.
The subject of the present book is that form of Yoga known as Raja-Yoga. The aphorisms of Patanjali are the highest authority on Raja-Yoga, and form its textbook. The other philosophers, though occasionally differing from Patanjali in some philosophical points, have, as a rule, acceded to his method of practice a decided consent. The first part of this book comprises several lectures to classes delivered by the present writer in New York. The second part is a rather free translation of the aphorisms (Sutras) of Patanjali, with a running commentary. Effort has been made to avoid technicalities as far as possible, and to keep to the free and easy style of conversation. In the first part some simple and specific directions are given for the student who wants to practice, but all such are especially and earnestly reminded that, with few exceptions, Yoga can only be safely learnt by direct contact with a teacher. If these conversations succeed in awakening a desire for further information on the subject, the teacher will not be wanting.
The system of Patanjali is based upon the system of the Sankhyas, the points of difference being very few. The two most important differences are, first, that Patanjali admits a Personal God in the form of a first teacher, while the only God the Sankhyas admit is a nearly perfected being, temporarily in charge of a cycle of creation. Second, the Yogis hold the mind to be equally all-pervading with the soul, or Purusha, and the Sankhyas do not.
It is sometimes mistakenly said that Sankaracharya taught that only the path of Jnana and scriptural study of Brahman was the way to enlightenment. This is not true. In his text, Aparoksanubhuti, Sankaracharya addresses what is needed in verses 100-129. In verses 100-105 he says (translator Swami Vimuktananda):
Now, for the attainment of the aforesaid (knowledge) I shall expound the fifteen steps by the help of which one should practice profound meditation at all times. [translator's note: these fifteen steps include the eight steps of Patanjali]
The Atman that is absolute existence and knowledge cannot be realized without constant practice. So one seeking after knowledge should long meditate upon Brahman for the attainment of the desired goal.
The steps, in order, are described as follows: the control of the senses, the control of the mind, renunciation, silence, space, time, posture, the restraining root (Mulabandha), the equipoise of the body, the firmness of vision, the control of the vital forces, the withdrawal of the mind, concentration, self-contemplation, and complete absorption.
The restraint of all the senses by means of such knowledge as "All is Brahman" is rightly called Yama which should be practiced again and again.
The continuous flow of only one kind of thought, to the exclusion of all other thoughts, is called Niyama, which is verily the supreme bliss and is regularly practiced by the wise.
Raja Yoga is also explained by Sri Krishna in the 6th chapter, The Yoga of Meditation, of the Gita. In a few of the verses from Chapter 6, the Lord says:
Let a man be lifted up by his own self; let him not lower himself, for he himself is his friend, and he himself is his enemy.
A yogi should always try to concentrate his mind, retiring into solitude and living alone, having subdued his mind and body and got rid of his desires and possessions.
11-12. In a clean spot having fixed his seat--a firm seat, neither too high nor too low--and having spread over it kusagrass, and then a dear skin, and then a cloth,
And sitting there, he should practice yoga for the purification of the self, restraining the activities of the mind and senses, and bringing his thoughts to a point.
He should sit firm, holding his body, neck, and head erect and still, and gaze steadily at the tip of the nose, without looking around.
Completely serene and fearless, steadfast in the vow of brahmachari, disciplined in mind, and ever thinking on Me, he should sit in yoga, regarding Me as his Supreme Goal.
Keeping himself ever steadfast in this manner, the yogi of subdued mind attains the Peace abiding in Me--the Peace that culminates in Nirvana.
Finally, Swami Vivekananda says (Complete Works, V7, p 197-198; and here under the title Conversations and Dialogues, sub-title I - XXIX, sub-sub-title XV - http://cwsv.belurmath.org/volume_7/vol_7_frame.htm):
Disciple: Sir, now you are speaking of Jnana; but sometimes you proclaim the superiority of Bhakti, sometimes of Karma, and sometimes of Yoga [meaning Raja]. This confuses our understanding.
Swamiji: Well, the truth is this. The knowledge of Brahman is the ultimate goal — the highest destiny of man. But man cannot remain absorbed in Brahman all the time. When he comes out of it, he must have something to engage himself. At that time he should do such work as will contribute to the real well-being of people. Therefore do I urge you in the service of Jivas in a spirit of oneness. But, my son, such are the intricacies of work, that even great saints are caught in them and become attached. Therefore work has to be done without any desire for results. This is the teaching of the Gita. But know that in the knowledge of Brahman there is no touch of any relation to work. Good works, at the most, purify the mind. Therefore has the commentator Shankara so sharply criticized the doctrine of the combination of Jnana and Karma. Some attain to the knowledge of Brahman by the means of unselfish work. This is also a means, but the end is the realization of Brahman. Know this thoroughly that the goal of the path of discrimination and of all other modes of practice is the realization of Brahman.
Disciple: Now, sir, please tell me about the utility of Raja-Yoga and Bhakti-Yoga.
Swamiji: Striving in these paths also some attain to the realisation of Brahman. The path of Bhakti or devotion of God is a slow process, but is easy of practice. In the path of Yoga there are many obstacles; perhaps the mind runs after psychic powers and thus draws you away from attaining your real nature. Only the path of Jnana is of quick fruition and the rationale of all other creeds; hence it is equally esteemed in all countries and all ages. But even in the path of discrimination [Jnana Yoga] there is the chance of the mind getting stuck in the interminable net of vain argumentation. Therefore along with it, meditation [Raja Yoga] should be practiced. By means of discrimination and meditation [Jnana and Raja], the goal or Brahman has to be reached. One is sure to reach the goal by practicing in this way. This, in my opinion, is the easy path ensuring quick success.