The Obligation Of This Tashahhud
Next, after completing the fourth rak'ah, he (صلى الله علیه وسلم) would sit for the last tashahhud. He would instruct regarding it, and do in it, just as he did in the first tashahhud, except that "he would sit mutawarrikan" , "with his left upper thigh on the ground, and both his feet protruding from one (i.e. the right) side."  "He would have his left foot under his (right) thigh and shin" , "his right foot upright"  or occasionally "he would lay it along the ground."  "His left palm would cover his (left) knee, leaning heavily on it."  [see diagram]
He set the example of sending prayers on him (صلى الله علیه وسلم) in this tashahhud, as in the first tashahhud; the ways of sending prayer on him (صلى الله علیه وسلم) narrated have been given in that section.
The Obligation Of Sending Prayers On The Prophet (صلى الله علیه وسلم) In This Tashahhud
Once, "he (صلى الله علیه وسلم) heard a man supplicating in his prayer without glorifying the majesty of Allaah Exalted, nor sending prayers on the Prophet (صلى الله علیه وسلم), so he said:
"This man has been hasty."
He then called him and said to him and others,
"When one of you prays, he should begin with the praise of his Lord, Sublime and Mighty, and his exultation, and then send prayers (in one narration: he should send prayers) on the Prophet (صلى الله علیه وسلم), and then supplicate as he wishes." " 
Also, "he heard a man glorifying and praising Allaah, and sending prayers on the Prophet (صلى الله علیه وسلم) in prayer, so the Messenger of Allaah (صلى الله علیه وسلم) said to him:
"Supplicate, and you will be answered; ask, and you will be given." " 
The Obligation To Seek Refuge From Four Things Before Supplicating
He (صلى الله علیه وسلم) used to say, "When one of you has finished the [last] tashahhud, he should seek refuge with Allaah from four things; [saying:
"O Allaah! I truly seek refuge with You] from the punishment of Hellfire, and from the punishment of the grave, and from the trials of living and dying, and from the evil [trials] of the False Christ." [Then he should supplicate for himself with what occurs to him.]" 
"He (صلى الله علیه وسلم) would supplicate with it in his own tashahhud." 
Also, "he used to teach the Companions (رضي الله عنهم) this the way he taught them Soorahs of the Qur'aan." 
Supplication Before The Salaam, & Its Various Types
He (صلى الله علیه وسلم) used to use different supplications in his prayer , supplicating with different ones at different times; he also endorsed other supplications, and "ordered the worshipper to select of them what he wishes."  They are:
- "O Allaah! call me to account with an easy reckoning." 
- "O Allaah! [I ask you], by Your knowledge of the Unseen, and Your control over the creation: give me life as long as You know that life is best for me, and take me when death is best for me. O Allaah! I also ask of You fear of You, in secret and in open; I ask of You the word of Truth (in one narration: Wisdom) and justice in anger and in pleasure; I ask of You moderation in poverty and affluence; I ask of You joy which does not fade; I ask of You pleasure [which does not pass away, nor that] which ceases; I ask of You contentment with Your decree; I ask of You coolness of life after death; I ask of You the delight of looking towards Your Face; and [I ask of You] eagerness towards meeting You, not in harmful adversity, nor in misleading afflictions. O Allaah! adorn us with the decoration of eemaan, and make us those who guide and are guided. 
- He taught Abu Bakr as-Siddeeq (رضي الله عنه) to say:"O Allaah! indeed I have wronged myself greatly, and none can forgive sins except You, so forgive me out of Your forgiveness, and have mercy on me. Truly, You are the Oft-Forgiving, the Most Merciful." 
- He instructed 'Aa'ishah (radi-Allaahu 'anhaa) to say:"O Allaah! indeed I ask of You all Good, [the imminent and the far-off,] that of it which I know and that which I do not know. I seek refuge with You from all Evil, [the imminent and the far-off,] that of it which I know and that which I do not know. I ask of You (in one narration: O Allaah! indeed I ask of You) the Garden, and whatever saying or deed which brings one near to it; I seek refuge with You from the Fire, and (from) whatever saying or deed which brings one near to it. I ask of You (in one narration: O Allaah! indeed I ask of You) [the] good of what was asked of You by Your slave and messenger [Muhammad; and I seek refuge with You from evil of what Your slave and messenger Muhammad (صلى الله علیه وسلم) sought refuge with You]. [I ask of You] that whatever You have decreed for me, its result [for me] be beneficial. 
- He said to a man, "What do you say during the prayer?"
He replied, "I bear witness (i.e. do the tashahhud), then I ask Allaah for the Garden, and I seek refuge with Him from the Fire. However, by Allaah, there is no murmuring  as good as yours or that of Mu'aadh." So he said,
"Our murmuring is like yours." 
- He heard a man saying in his tashahhud:"O Allaah! indeed I ask of You, O Allaah (in one narration: by Allaah), the One, the Only, the Absolute, Who begets not and nor is He begotten, and there is none like Him, that You forgive me my sins; indeed You are the Oft-Forgiving, Most Merciful.
On this, he (صلى الله علیه وسلم) said,
"He has been forgiven, he has been forgiven." 
- He heard another man say in his tashahhud:"O Allaah! Indeed, I ask of You, by the fact that to You belongs all Praise; there is no (true) god except You, [You alone, You have no partners;] the Bestower of Favours; [O] Originator of the Heavens and the Earth; O One that is Full of Majesty and Honour; O Living One, O Eternal One; [indeed I ask of You] [the Garden, and I seek refuge with You from the Fire]."
[So the Prophet (صلى الله علیه وسلم) said to his Companions,
Do you know with what he has supplicated?
They said, "Allaah and His Messenger know best." He said,
- One of the last things he would say between the tashahhud and the tasleem would be:"O Allaah! Forgive me what I have done in the past, and what I will do in the future, and what I have concealed, and what I have done openly, and what I have exceeded in, whatever You know about more know than I. You are the Bringer-Forward, and You are the Delayer, there is no (true) god except You." 
 ibid. As for two-rak`ah prayers such as Fajr, the Sunnah is to sit muftarishan. This difference in detail is documented from Imaam Ahmad, cf. Ibn Hani's Masaa'il of Imaam Ahmad (p. 79).
 Abu Daawood & Baihaqi with a saheeh sanad.
 Muslim & Abu `Awaanah.
 Ahmad, Abu Daawood, Ibn Khuzaimah (1/83/2) & al-Haakim, who declared it saheeh and Dhahabi agreed.
It should be known that this hadeeth proves that salaah (sending prayers) on the Prophet (صلى الله علیه وسلم) in this tashahhud is obligatory, due to the command about it. This opinion was taken by Imaam Shaafi`i and by Imaam Ahmad in the later of the two narrations from him, and before them by several Companions, as well as other people of knowledge. Because of this, Aajuri said in Sharee`ah (p. 415):
"He who does not send prayers on the Prophet (صلى الله علیه وسلم) in the final tashahhud must repeat the prayer."
Hence, those who label Imaam Shaafi`i as being alone and odd in his opinion on this, are not being just, as the faqeeh Haitami has explained in Darr al-Mandood (sections 13-16).
 Nasaa'i with a saheeh sanad.
 Muslim, Abu `Awaanah, Nasaa'i & Ibn al-Jaarood in al-Muntaqaa (27). It is given in Irwaa' (350).
 Abu Daawood & Ahmad with a saheeh sanad.
 Muslim & Abu `Awaanah.
 We have not said, "... in his tashahhud" because the text is "... in his prayer", not specifying either tashahhud or anything else. Hence, it covers all positions suitable for supplication, e.g. prostration and tashahhud; the instruction to supplicate in these two postures has been mentioned.
 Bukhaari & Muslim. Athram said,
"I asked Ahmad: 'With what (words) should I supplicate after tashahhud ?' He said, 'As has been narrated.' I said, 'Didn't the Messenger of Allaah (صلى الله علیه وسلم) say, "Then he should select whichever supplication he likes" ?' He said, 'He should select out of what has been narrated.' I repeated the question: he said, 'From what has been narrated'."
This was quoted by Ibn Taymiyyah (Majmoo` al-Fataawaa 69/218/1), who endorsed it, adding,
"Hence, 'whichever supplication' refers to the supplications which Allaah loves, not to any supplication ..."
Later he said,
"Hence, it is best to say: (one should supplicate) with the approved, established supplications, and these are what have ben narrated and those that are beneficial."
This is so, but to recognise which supplications are indeed beneficial depends on authentic knowledge, and this is rarely found among the people, so it is best to stick to the supplications quoted, especially when they include what the worshipper wishes to request. Allaah knows best.
 ma'tham: what causes a man to sin, or the sin itself.
155 maghram: burden; here it means debt, as proved by the rest of the hadeeth, in which `Aa'ishah said, "Someone said to him, `Why do you seek refuge from maghram, so often, O Messenger of Allaah ?' He replied,
Truly, when a man becomes indebted, he speaks and lies, and he promises and breaks his promise.
 Bukhaari & Muslim.
 i.e. from the evil of the bad actions I have done, and from the evil of not doing good actions.
 Nasaa'i with a saheeh sanad & Ibn Abi `Aasim in his as-Sunnah (no. 370 - with my checking); the addition is from the latter.
 Ahmad & Haakim who declared it saheeh and Dhahabi agreed.
 Nasaa'i & al-Haakim who declared it saheeh and Dhahabi agreed.
 Bukhaari & Muslim.
 Ahmad, Tayaalisi, Bukhaari in al-Adab al-Mufrad, Ibn Maajah & Haakim who declared it saheeh and Dhahabi agreed. I have given its takhreej in Silsilah al-Ahaadeeth as-Saheehah (1542).
 dandanah: to speak such the intonation is audible, but the words are incomprehensible - in this case, the quiet words of supplication. The final statement means, "Our words are like yours."
 Abu Daawood, Ibn Maajah & Ibn Khuzaimah (1/87/1) with a saheeh isnaad.
 Abu Daawood, Nasaa'i, Ahmad & Ibn Khuzaimah; Haakim declared it saheeh and Dhahabi agreed.
 This is tawassul (a seeking of approach) to Allaah through His most beautiful names and attributes, and this is what Allaah the Exalted commands:
"To Allaah belong the most beautiful names, so call on Him by them." (A`raaf 7:180)
As for seeking to approaching Allaah through other things, e.g. for so-and-so's sake, or by so-and-so's right, status, dignity, etc., there is text from Imaam Abu Haneefah - (رحمه الله) - and his companions that such a practice is at least disliked (makrooh); in general it is prohibited (haraam). Therefore, it is a pity that one sees most of the people, among them many shaykhs, totally neglecting the approved tawassul, - you will never hear them approaching Allaah this way - but they are well-versed in innovated forms of tawassul, which are at the very least debatable, as though no other way is allowed!
Shaykh-ul-Islaam Ibn Taymiyyah has composed an extremely good essay on this subject entitled Tawassul and Waseelah ("Approaching Allaah, and the Means of doing so"), which should be consulted, for it is very important, and there is little to compare with it in its coverage. There is also my article Tawassul - its types and its rules, which is also important in its subject-matter and format, and also refutes some of the latest misconceptions advanced by contemporary doctors of religion. May Allaah guide us and them.
 Abu Daawood, Nasaa'i, Ahmad, Bukhaari in al-Adab al-Mufrad, Tabaraani & Ibn Mandah in Tawheed (44/2, 67/1, 70/1-2) with saheeh isnaads.
 Muslim & Abu `Awaanah.