I have always been fascinated by the section of the fabulous "Yoga Sutras" which describe the "siddhis" (psionic powers). Sri Patanjali did a marvelous task of organizing and codifying the Yoga Darshan during the ancient aeon. Do the Scriptures explain how these "siddhis" work? Are they to be taken literally or are they metaphorical and allegorical?
There is very detail description and explanation of Various Siddhis a yogi can achieve & ways in the Purana called "Shreemad Bhagvat Puran" (Canto 11 Chapter 15 ) This whole chapter of 36 verses is about Siddhis.
The names of various Siddhis descibed are-:
1) Anima (अणिमा) , 2) Mahima (महिमा) 3) Laghima (लघिमा) 4) Prapti ( प्राप्ति) 5) Prakamya (प्राकाम्य) 6) Vashita (वशिता) 7) Ishita (इशिता) 8) Kaamvasyita (कामवसयिता) 9) Doorshrvan (दूरश्रवण) 10) Doordarshan (दूरदर्शन) 11) Manojava (मनोजव)
Here are some the Verses of Siddhies and description of them -
महत्यातन्मयि परे यथासंस्थम मनो दधत ।
महिमा नवाप्नोति भूतानां च पृथक पृथक ॥
MahatyaNmayi Pare YathaSanSthama Mano Dadhat MahimaNavapnoti Bhutanam cha Pruthak Pruthak
Meaning - One who absorbs his mind in the particular form of the mahat-tattva and thus meditates upon Me as the Supreme Soul of the total material existence achieves the mystic perfection called mahimā. By further absorbing the mind in the situation of each individual element such as the sky, air, fire, and so on, one progressively acquires the greatness of each material element.
परमाणुमये चित्तं भूतानां मयि रञ्जयन ।
कालसूक्ष्मार्थतां योगी लघिमानवाप्नुयात ॥12॥
ParamanuMaye Chittam Bhutanam Mayi Rajrayan KaalSukshmaRthaTaam Yogi LaghimanVapnuyat
Meaning - I exist within everything, and I am therefore the essence of the atomic constituents of material elements. By attaching his mind to Me in this form, the yogī may achieve the perfection called laghimā, by which he realizes the subtle atomic substance of time.
धारयन मैय्यहंतत्वे मनो वैकरिकेs खिलम ।
सर्वेंद्रियाणामात्मत्वम प्राप्तिमं प्राप्नोति मन्मना: ॥13॥
Dharayan MaiyaaHamTatve Mano Vaikarike Khilam ServendriyanaMaaMatvham Praptim Prapnoti Manmana
Meaning - Fixing his mind completely in Me within the element of false ego generated from the mode of goodness, the yogī obtains the power of mystic acquisition, by which he becomes the proprietor of the senses of all living entities. He obtains such perfection because his mind is absorbed in Me.
महत्यात्मनि य: सुत्रे धारयेन्मयी मानसं ।
प्राकाम्यम पारमेष्ठयम में विन्दतेs व्यक्तजन्मन: ॥14॥
Mahattyatmni ya Sutre Dharayenmayi Maanasam Prakamyam Paarmeshtam Me Vindate VyaktaJanmanah
Meaning - One who concentrates all mental activities in Me as the Supersoul of that phase of the mahat-tattva which manifests the chain of fruitive activities obtains from Me, whose appearance is beyond material perception, the most excellent mystic perfection called prākāmya.
मैय्याकाशात्मनि प्राणे मनसा घोषमुद्वहन ।
तत्रोपलब्धा भुतानां हंसो वाच: शृणोत्यसौ ॥19॥
MaiyaKashaTamni Prano Manasa GhoshmudvaHan Tatropalabdha Bhutaanam Hanso Vachah ShrunoTyasau
Meaning - That purified living entity who fixes his mind on the extraordinary sound vibrations occurring within Me as the personified sky and total life air is then able to perceive within the sky the speaking of all living entities.
मनो मयि सुसंयोज्य देहं तदनु वायुना ।
मद्धरणानुभावेन तत्रात्मा यत्र वै मनः ॥21॥
Mano Mayi SusamYojya Deham Tadanu Vayuna MatDhaaranaBhavena Tatratma Yatra Vai Manh
Meaning - The yogī who completely absorbs his mind in Me, and who then makes use of the wind that follows the mind to absorb the material body in Me, obtains through the potency of meditation on Me the mystic perfection by which his body immediately follows his mind wherever it goes.
You can browse through all the contains of the chapter called "Lord Kṛṣṇa’s Description of Mystic Yoga Perfections" (SB 11.15) Here