About Nyaas
Well, Nyaas literally means establishing? We establish Divine energies at various parts of body, fingers, direction, or even Mantra syllables. Nyaas can be of many types. Each Mantra has its own corresponding Nyaas Vidhi. It can be like Rishi Nyaas, Kar Nyaas, Hridaya / Shad Ang Nyaas, Varn Nyaas, Stithi Nyaas, Srishti Nyaas.... so depending on the Mantra its Nyaas is done. Still the first three Nyaas (Rishi Nyaas, Kar Nyaas and Shad Ang Nyaas) are usually bare minimum to perform before the Jaap of a Mantra. Usually, because for some Mantra, like of Shakti Mantra, Nyaas is done in genital and Nyaas for Beej Mantra in feet... and so on, so it all varies from Mantra to Mantra

For the sake of simplicity, I have added a file named "Mantra 7 Secret" in the files section, please download it.

Rishi Nyaas is done by touching tips of 5 finger of right hand on (while chanting); Divine Grace establishment of parts of Viniyog
Third Eye (forehead) for Rishi Name (Rishaye Namah Shirasi)
Mouth/throat for Chhand (Chhand namah mukhe)
Heart for Devta (Devta namah hridi)
Genital for Beej (Beejam namah ghooye/Linge)
Feet for Shakti (shaktye nmah paadyo)
Navel for Keelakam (kelkay namah naabhau)
All part at once (.... Viniyogay namah sarvaange)

Kar Nyaas is done by (with chanting of Beej Mantra Roop, example of "Shreem" Beej in bracket); Energy Establishment in Fingers
First joining thumb to index finger ( shraam angushtabhyaam namah)
Indx finger to thumb ( shreem tarjaneebhyaam namah)
Thumb to middle dinger ( shroom madhyamaa bhyaam namah)
to ring finger ( shraim anaamikaabhyaam namah)
to little finger( shraum kanishkaabhyaam namah)
Finally joining base of both fists and pranaam ( sh-rah kartal karprishtaabhyaam namah)

Hridayaadi/Shad Ang Nyaas is done by using right hand to touch 6 body parts
Base of first to Heart (shraam hridyaya namah)
Five finger tips to Forehead (shreem Shirasay swaahaa)
Thumb to Braid base (Shroom shikhaayai vashat)
Both palms on opposite shoulder (shraim kavachay hoom)
Both hand First two fingers on Eyes (shraum Netra taraya Vausht)
Left palm straight, rotate right hand over head with first two fingers straight and other bend (shrah astraya phat)
Snap on all side, saying "Iti Digbandh".

Varn Nyaas - This Nyaas differs for various Mantra, so it depends on the Mantra

Purpose of Nyaas
Well Nyaas gives support (Saanidhya) of Divine masters and energies to ensure your success. It establishes vital energies in vital body parts enhancing your chance of becoming Mantra Chaitanya. Although Mantra Bhaavanaa is very important, but that does not mean one should ignore other procedures if they are known... At the end of the day, Mantra Chetanaa is the main thing... all these Nyaas, Mudraa Dhyaan etc are also meant to help Saadhak become truly Mantra Chaitanya, one with vibration... ie feelings, image and surrender. And if you don't succeed once (no one does in one go), keep trying... "Persistence overcome all known obstacles to mankind."

(1) Rishi Nyaas (Divine Grace establishment of parts of Viniyog)
(2) Kar Nyaas (Energy Establishment in fingers)
(3) Hridi / Shad-Ang Nyaas (Energy Establishment in 6 Body parts)... Then any other type of Nyaas if need be, especially Dig Nyaas (10 direction locking by establishing energies in 10 directions around you)
(4) Then comes Dhyaan (Meditation on image of the Deity with apt Dhyaan Mantra)
(5) Then comes Aavaahan (Invoking the main deity in corresponding idol or picture or Yantra of that particular Mantra)
(6) Then Mudraa (Hand or body posture to please the deity)
(7) Then Shakti Peeth Poojaa and / or Yantra Aavaran Poojaa if need be
(8) Then Poojaa (making offerings, 5 or 16 or 18... 64)
(9) Then Mantra Jap (Chanting)
(10) Then Stotra and / or Aaratee (hymn to please deity)
(11) Then Kshamaa Praarthanaa (ask for forgiveness)
(12) Finally, Jal or Prasaad Vitaran (distributing water or offering left after ritual)

Do this everyday till your Jap is complete, then another Sankalp for Jap in lieu of Havan and finally Tarpan, then Maarjan, then Braahman Bhojan on the last day.

General Structure of Mantra Saadhanaa

(1) Viniyog
First of all, before any Mantra chanting, you have to hold water in a teaspoon or palm, announce these parts of a Mantra, and then at end of it, let water flow on earth, as symbolic of the resolution being absorbed by earth and cosmos. This is called Viniyog.

Even without knowledge or knowledge of Keelak also you can use a Mantra provided you have at least first 6 part of Viniyog -
(1) Rishi (Creator of Mantra, Seer who first attained or mastered the Mantra)
(2) Chhand (Meter of Mantra or pattern of pronunciation)
(3) Devataa (Name of deity)
(4) Beejam (main seed for power source of Mantra)
(5) Shakti (you can say main power enhancer, like to mature the seed)
(6) Keelak (the unlocking password)
(7) Abheesht Arth  (your purpose of chanting)

(2) Nyaas   see above, do 3 Nyaas - Rishi Nyaas, Kar Nyaas and Shad Ang Nyaas. Nyaas is a must, in fact a double must when you add something in Viniyog as a specific purpose, because its well know fact, when you just say "to please Diety I chant", then you may skip Nyaas and other procedure, but when you say "to please this Deity and get this wish fulfilled", then it becomes Sa-kaam Praarthnaa (prayer with desire), then Saadhanaa becomes Klisht and Mantra becomes your enemy, would even try to give you physical discomfort by the vibrations if you don't have proper grace of your Guru and Nyaas of seers, so one has to be very careful. Thats why, even before Viniyog of the main Mantra, consider Guru, Ganesh and Kul Dev Poojan are a must. It may be very short but consider it a must.

(3) Dhyaan -
After Nyaas comes Dhyaan, It is meditation on Image of the Deity with apt Dhyaan Mantra. Then the Dhyaan Mantra (concentrating on deity image as written in Mantra on third eye) and then Mudraa before jap (please don't ask this, its a an important part just know that because five fingers mean 5 elements, you should create right element energies to invoke the Deity)

(4) Aaavaahan
Then Comes Aavaahan - Invoking the main deity in corresponding idol or picture or Yantra of that particular Mantra

(5) Mudraa
Then cmes Mudraa - Hand and body posture to please the Deity. Procedure and Mudraa for doing Nyaas differs from Mantra to Mantra, but usually the tip of five fingers like in "ShukreeMudra" is used to physically touch the body parts and then imagine energy flow with the Mantra vibration.

(6) Shakti Peeth Poojaa
Then comes Shakti Peeth Puja and or Yantra Aavaran Poojaa if need be

(7) Poojaa
Then Poojaa is performed making offerings, 5 or 16 or 18... 64 items

(8) Mantra Jaap
Then do Mantra Jap - Mantra chanting

(9) Stotra Recitation
Then recite Stotra - hymn to please deity

(10) Kavach (Armor)
Then read Kavach - wearing astral armour by special hymn

(11) Kshamaa Praarthanaa
Then Kshamaa Praarthanaa is to be asked for any known or unknown mistakes made during the Poojaa - ask for forgiveness

(12) Prasaad
Finally, Jal or Prasad Vitaran - distributing water or offering left after ritual

Mantra Viniyog

Chhand
Chhand or meter of Mantra is the pattern of pronunciation, Knowledge of meter of a Mantra is of paramount importance, because unless you know the right pronunciation of Mantra, everything ahead of that, no matter how precise other parts of ritual maybe, the whole ritual of Mantra Saadhanaa will be a failure.

Mantra Parts

Every Mantra has five parts - they are explained here with the reference of Mahaa Mrityunjaya Mantra -
Om Tryambakam Yajaamahe Sugandhim Pushtivardhanam
Urvaa Rukmev Bandhanaat Mrityormuksheeya Maamritaat

(1) Rishi (Guru or teacher of the Mantra), or Shir (head) - in this case it is Vashishth Jee
(2) Chhand (meter), or Mukh (mouth) - which is technically very specific for each Mantra - in this case it is Anushtup Chhand. This is a meter of four lines, with 8 phonemes each. It may be noted that any change in this meter shall cause distortion shall be ruined.
(3) Devataa (the deity of the Mantra), or Hridaya (heart) - in this case its Devataa is Lord Shiv -  Mrityunjaya Tryambakeshwar, the Jyotirling.
(4) Beej (the seed syllable that created the Mantra and contains the Mantra within itself, like the seed that creates the tree)  - Ling (the sexual organ) - there are several opinion about this but the most appropriate one is given by Kahol Rishi as "Haum"
(5) Shakti (physical power of the Mantra like the mother) - in this case Shakti is Devee Amriteshwaree Devee addressed as "Hreem"

Dhyaan Mantra is same as the one written in Dainik Guru Poojan book (the one you should have got with Deekshaa). (it is the same Mantra in Yagya Vidhaan also). After that, do proper Shodash Upachaar Poojaa of Guru in Guru Yantra. The general structure of a Mantrokt Saadhanaa is --

Start Saadhanaa

(1) First of all, before any Mantra chanting, you have to hold water in a teaspoon or palm, announce these parts of a Mantra, and then at end of it, let water flow on earth, as symbolic of the resolution being absorbed by earth and cosmos.
Do all Kriyaa from Pavitreekaran to Ganesh Smaran as in Dainik Guru Poojan, then take Sankalp for whole Saadhanaa on the first day --

Starting Day = Thursday (Guru Vaar), and theme of Saadhanaa is Yellow

(1) In Guru Poojan, First do Kavach Paath (as giving in Dainik Vidhaan (wearing astral amour by special hymn, for protecting you throughout the Saadhanaa)
(2) Viniyog (declaration) - before any Mantra chanting, hold water in a teaspoon or palm, announce these parts of a Mantra (Viniyog), and then at end of it, let water flow on earth, as symbolic of the resolution being absorbed by earth and cosmos. Parts of Viniyog are --
(a) Rishi (Seer who first attained or mastered the Mantra)
(b) Chhand (meter of Mantra = pattern of pronunciation)
(c) Mantra's Devta (Deity)
(d) Beej (seed, power source of Mantra)
(e) Shakti (enhancing power, like to mature the seed)
(f) Keelak (unlocking password)
(g) Abheesht Arth (your purpose of chanting)