First of all one has to legally obtain the mantra through initiation (Diksha). This is the first step. Next, Purascharan, as prescribed, has to be done.
Without Purascharana, a mantra is stated to be devoid of any powers.
The Puras’charanam of Gâyatrî is repeating this twenty four lakh times
(i.e., as many lakh times as there are syllables in the ...
Yes, except the mantras like "Hare Rama, Hare Krishna" or "Om Namo Narayana" given by saints like Chaitnaya Mahaprabhu, Ramanujacharya to entire mankind, all other mantras need initiation, even if they are simple Gayatri Mantra or "Om".
D: “Can anyone get any benefit by repeating sacred syllables (mantras)
picked up casually?
Similarly Just like the Tantric scriptures the goddess "Tvarita" is also discussed in puranas , we find very detailed description of her in Agni Purana. Below are the chapter names from Agni Purana.
1) Agni Purana - Part 2 - Chapter 147 - Mode of worshiping goddess Tvarita and others.
2) Agni Purana - Part 3 - Chapter 309 - Mode of worshiping ...
I can give a partial answer here.
TvaritA is so called because she gives results quickly (from the word tvarita meaning quick).
I know her mode of worship which is Tantric in nature and the relevant verses are quoted in the Brihat TantrasArah. The text however does not specify which of the Tantras it is quoting from.
Atha tvaritA mantrah ||
The word mantra in Sanskrit means ‘that which protects by being meditated upon’ (mananAt trAyate iti mantrah).
Mantra can contain bijAksharAs and name of the deity.
Example: chAmundA mantra ॐ ऐं ह्रीं क्लीं चामुण्डायै विच्चे।
Ganapati mantra : ॐ Gam Ganapataye Namaha
or may contain words like gAyatri mantra:
ॐ भूर् भुवः स्वः ।
You can find it on http://muktalib5.org/digital_library_secure_entry.htm
in brhattantrasāra :
"oṃ tatsaviturvareṇyaṃ tryambakaṃ yajāmahe sugandhiṃ
puṣṭivarddhaṇaṃ bhargo devasya dhīmahi urvārukamivabandhanāt
dhiyo yo naḥ pracodayāt (mṛtyormukṣīyamāmṛtāt)"
There is a mantra for Indra to be found in the ancient Indian tradition of Natya-Shastra. Before any performance in the theater, it was customary to worship (puja) and offer certain food articles to the gods and deities. This ceremony was considered “as meritorious as a Vedic sacrifice”.
For Indra, the specific mantra runs as follows: