How does a Guru uplift the disciple? How does the Liberated Soul lead the aspirant to spiritual realization ? What are the methods employed by the Guru? These are some insights on this question gathered from the works of Sri Aurobindo, The Mother (Mira Alfassa) and Ramana Maharshi.
The Guru is someone who has liberated his/her consciousness and has become an embodiment of the Divine. The Mother said that the Guru is a channel for the Divine who connects the aspirant to the Divine Power flowing through him –
Ultimately, what does the guru do? He connects (gesture of junction), he is nothing but a link. It’s not “his” power he gives you (that’s what he thinks, but it’s not true): he is the link. He brings you into contact with the Power – a contact you don’t have without him. But those who don’t need a guru will make contact WITHOUT a guru. Basically, the guru’s real power is to fill up the gaps! To bring you into contact: when you are in the higher planes, to bring you into contact with the Highest. Or to bring you into contact with your soul, your psychic being within, or to bring you into contact with the Supreme – but that not many can do.
The Mother, Mother’s Agenda: July 10, 1963
Initiation (Diksha) by Emanation
The Guru is no longer bound to his physical body; He has a liberated consciousness and has the power to put an emanation of his consciousness into the disciple. An emanation is a portion of the Guru’s consciousness which merges with the disciple’s consciousness and allows the Guru to influence the disciple from within as required. M.P. Pandit, a disciple of Sri Aurobindo, writes in his book Gems of Tantra
When the Guru initiates, he puts out an emanation of the Power active in himself into the being of the disciple. This tapas-force begins the sadhana and leads the seeker on the path. The working of this Force is twofold: negatively, it weakens the hold of the lower obstructive nature and gradually dissipates the old samskaras, habits and impressions, leading eventually to the snapping of the knots of ignorance and ego that bind the soul; positively, it builds up a consciousness that grows through purification, subtilization and spiritualisation into the very nature of the Divine Consciousness that is sought for. 
The nature and purpose of the emanation was also explained by Sri Aurobindo in the book The Mother. While the description below pertains to the Mother, it can also apply to other Gurus who may use the same technique.
The emanation is not a deputy, but the Mother herself. She is not bound to her body, but can put herself out (emanate) in any way she likes. What emanates, suits itself to the nature of the personal relation she has with the Sadhak (seeker) which is different with each, but that does not prevent it from being herself. Its presence with the Sadhak is not dependent on his consciousness of it.
Sri Aurobindo, The Mother: The Mother’s Emanations
By virtue of this emanation, the Guru can identify his /her consciousness with that of the disciple’s and select the right Mantra that may be needed at the current stage of development.
The Guru-disciple relationship
Sri Aurobindo writes in the Synthesis of Yoga that the Guru awakens the disciple by three methods, each more powerful than the previous Sri Aurobindo, The Synthesis of Yoga – I: The Four Aids :
Teaching : The teacher does not seek to impose his/her opinions on the passive receptive mind of the disciple. Instead, the teacher throws in suggestions which are productive at the current stage of development of the aspirant. The Guru seeks to awaken rather than to instruct; he aims at the growth of the faculties and the experiences by a natural process and free expansion.
Example : The Example is more powerful than the Teaching. Example does not mean the Guru’s outward acts or personal character but the spiritual realization which the Guru has attained. The Guru acts as an Exemplar who stimulates aspiration within the disciple to progress higher up the ladder of Evolution.
Influence : The most powerful method is the method of Influence. This does not imply outward authority but power of contact, of his presence, of the nearness of his soul to the soul of another, infusing into it, even though in silence, that which he himself is and possesses. The greatest Master is much less a Teacher than a Presence pouring the divine consciousness and its constituting light and power and purity and bliss into all who are receptive around him. This method can be illustrated in the life of Ramana Maharshi, the sage of Arunachala, who gave his teaching in Silence. This is an excerpt from his talks –
Question: How can silence be so powerful?
Sri Ramana Maharshi: A realised one sends out waves of spiritual influence, which draw many people towards him. Yet he may sit in a cave and maintain complete silence. We may listen to lectures upon truth and come away with hardly any grasp of the subject, but to come into contact with a realised one, though he speaks nothing, will give much more grasp of the subject. He never needs to go out among the public. If necessary he can use others as instruments. The Guru is the bestower of silence who reveals the light of Self-knowledge that shines as the residual reality. Spoken words are of no use whatsoever if the eyes of the Guru meet the eyes of the disciple.
Question: Why does Bhagavan (i.e. Ramana Maharshi) not go about and preach the truth to the people at large?
Sri Ramana Maharshi: How do you know I am not doing it? Does preaching consist in mounting a platform and haranguing the people around? Preaching is simple communication of knowledge; it can really be done in silence only. What do you think of a man who listens to a sermon for an hour and goes away without having been impressed by it so as to change his life? Compare him with another, who sits in a holy presence and goes away after some time with his outlook on life totally changed. Which is the better, to preach loudly without effect or to sit silently sending out inner force? Again, how does speech arise? First there is abstract knowledge. Out of this arises the ego, which in turn gives rise to thought, and thought to the spoken word. So the word is the great grandson of the original source. If the word can produce an effect, judge for yourself how much more powerful must be the preaching through silence. 
How does this Silence act on the disciple’s consciousness ? We have a clue from Sri Aurobindo’s Record of Yoga, where he has mentioned that the Guru uses occult power of Vyapti (Sanskrit for all-pervasiveness) to communicate by subtle means with the disciple. See the Sapta-Chatushthaya for more on Vyapti and Prakamya.
By Prakamya we have perception of another’s feelings; by Vyapti these feelings are felt striking on our own consciousness or ours are thrown into another. It is possible by vyapti to communicate anything we have in our systems – thought, feeling, power, etc – to another and if he is able to seize and hold it, he can make it his own & use it. The teacher & the guru habitually use this power of vyapti which is far more effective than speech and writing. Every thought, feeling, sensation or other movement of consciousness in us creates a wave or current which carries it out into the world-consciousness around and there it enters in any adhara (support) which is able and allowed to receive it.
Sri Aurobindo, Record of Yoga – I: Sapta Chatusthaya
In addition to this, M.P. Pandit describes Sparsha-Diksha (initiation by touch) in his book Gems of Tantra
…the most valuable (method of the Guru) is the physical touch of his/her hand. There are certain obstinate physical and subtle-physical samskaras( i.e. residues of the past), associations and habits, which are difficult for the seeker to get rid of unaided. They can be removed only by the direct power of the Guru flowing through a physical channel. On this plane of physical matter, the importance of physical means cannot be gainsaid. Under certain circumstances physical means alone are fully effective. The means have to correspond to the plane of existence that is being worked upon. The physical touch of the Guru sets into current a dynamis that strikes at the sources of the physical obstructions, eliminates them from the source and enables the spiritual Power to transform the human material into the divine. 
It is also relevant here to take an example from antiquity. The various Vidyas given in the Upanishads were imparted by the Guru to the disciple by subtle means (i.e. thought transference). These Vidyas were seed-principles (i.e. realize the Divine as Bliss, or realize the Divine as the immutable Self) that disciple had to realize within his consciousness through meditation. For more on this, see the post Vidyas in the Upanishads
- M.P. Pandit. Gems on Tantra volume 2, p 27
- Pandit. op. cit., p 48