What to Say in Tashahhud
Question

I want to know the wording of the Tashahhud in prayer, and how to send blessings on the Prophet (peace and blessings of Allah be upon him).
Praise be to Allah.Importance of learning the rulings of prayer
The Messenger (peace and blessings of Allah be upon him) encouraged us to learn the rulings on prayer and how he (peace and blessings of Allah be upon him) prayed, so that we would follow his example in that. He said: “Pray as you have seen me praying.” (Narrated by Al-Bukhari, 631) 
Based on this, we must pay attention to learning this. 
Significance of multiple versions of Tashahhud
The wordings for the Tashahhud and the blessings on the Prophet (peace and blessings of Allah be upon him) that have been narrated in reports are many and various. It is best for the Muslim to recite all of them, saying it in one form on one occasion and in another form on another occasion, and so on, so that he will have done all the sunnahs. He should not limit himself only to some of them. But if that is too hard for him, then he should stick to what he is able to do, and there is no sin on him in sha Allah. 
What to say in Tashahhud
There follow some of the versions of the Tashahhud and blessings on the Prophet (peace and blessings of Allah be upon him) that have been narrated in proven reports from the Prophet (peace and blessings of Allah be upon him) in the prayer.

Ibn Mas`ud (may Allah be pleased with him) recited the Tashahhud as follows:  At-tahiyyatu Lillahi was-salawatu wat-tayyibat, as-salamu `alayka ayyuhan-Nabiyyu wa rahmat-Allahi wa barakatuhu. As-salamu `alayna wa `ala `ibadillah As-salihin. Ash-hadu allaa ilaha illallah wa ash-hadu anna Muhammadan `abduhu wa rasuluhu (All compliments, prayers and pure words are due to Allah. Peace be upon you, O Prophet, and the mercy of Allah and His blessings. Peace be upon us, and on the righteous slaves of Allah. I bear witness that none has the right to be worshipped except Allah, and I bear witness that Muhammad is His slave and Messenger). (Narrated by Al-Bukhari, 6265 and Muslim, 402)
Ibn `Umar (may Allah be pleased with him) recited the Tashahhud as follows: At-tahiyyatu Lillahi was-salawatu wat-tayyibat, as-salamu `alayka ayyuhan-Nabiyyu wa rahmat-Allahi wa barakatuhu. As-salamu `alayna wa `ala `ibadillah As-salihin. Ash-hadu alla ilaha illallah wahdahu la sharika lah wa ash-hadu anna Muhammadan `abduhu wa rasuluhu (All compliments, prayers and pure words are due to Allah. Peace be upon you, O Prophet, and the mercy of Allah and His blessings. Peace be upon us, and on the righteous slaves of Allah. I bear witness that none has the right to be worshipped except Allah alone with no partner or associate, and I bear witness that Muhammad is His slave and Messenger). (Narrated by Abu Dawud, 971 and classed as authentic by Al-Albani) 
The Tashahhud of `Umar was recited by him on the pulpit in order to teach the people: “At-tahiyyatu Lillahi, az-zakiyatu Lillahi, Al-tayyibatu Lillahi, As-salawatu Lillahi. As-salamu `alayka ayyuhan-Nabiyyu wa rahmat-Allahi wa barakatuhu. As-salamu `alayna wa `ala `ibadillah As-salihin. Ash-hadu alla ilaha illallah wa ash-hadu anna Muhammadan `abduhu wa rasuluhu (All compliments are due to Allah, all pure things are due to Allah, all pure words are due to Allah, all prayers are due to Allah. Peace be upon you, O Prophet, and the mercy of Allah and His blessings. Peace be upon us, and on the righteous slaves of Allah. I bear witness that none has the right to be worshipped except Allah, and I bear witness that Muhammad is His slave and Messenger). (Narrated by Malik, 204 and classed as authentic by Al-Albani)

How to send blessings on the Prophet in prayer
As for the wording of the blessings on the Prophet (peace and blessings of Allah be upon him), it is as follows: 
“Allahumma salli `ala Muhammad wa `ala ali Muhammad kama sallayta `ala Ibrahim wa `ala ali Ibrahim, innaka hamidun majid. Allahumma barik `ala Muhammad wa `ala ali Muhammad kama barakta `ala Ibrahim wa `ala ali Ibrahim, innaka hamidun majid (O Allah, send prayers upon Muhammad and upon the family of Muhammad, as You sent prayers upon Ibrahim and upon the family of Ibrahim; You are indeed Worthy of Praise, Full of Glory. O Allah, send blessings upon Muhammad and upon the family of Muhammad as You sent blessings upon Ibrahim and upon the family of Ibrahim; You are indeed Worthy of Praise, Full of Glory).” (Narrated by Al-Bukhari, 3370)
“Allahumma salli `ala Muhammad wa `ala ali Muhammad kama sallayta `ala ali Ibrahim, wa barik `ala Muhammad wa `ala ali Muhammad kama barakta `ala ali Ibrahim fil-`alamin, innaka hamidun majid (O Allah, send prayers upon Muhammad and the family of Muhammad, and send blessings upon Muhammad and the family of Muhammad, as You sent prayers and blessings upon Ibrahim and the family of Ibrahim among the nations; You are indeed Worthy of Praise, Full of Glory).”
And Allah knows best.