Source : Central-mosque.com / 27 Sep 2014

Allah (SWT) takes an Oath by the Ten Nights of Dhul-Hijja1h:

(وَٱلۡفَجۡرِ(١) وَلَيَالٍعَشۡرٍ۬(٢

I swear by the dawn, [89:1] and by the Ten Nights, [89:2]

قَالَهُعَلِيّوَابْنعَبَّاسوَعِكْرِمَةوَمُجَاهِدوَالسُّدِّيّوَعَنْمَسْرُوقوَمُحَمَّدبْنكَعْبالْمُرَادبِهِفَجْريَوْمالنَّحْرخَاصَّة

Some commentators, like Mujahid and 'Ikramah, refer this to the dawn of 'the Day of Sacrifice' on the tenth of Dhul Hijjah. A narration from Sayyidna Ibn 'Abbas (RA) concurs with this view. (Summarised from Tasfeer Maariful Qur'aan & Tafseer Ibn Katheer)

وَاللَّيَالِيالْعَشْرالْمُرَادبِهَاعَشْرذِيالْحِجَّةكَمَاقَالَهُاِبْنعَبَّاسوَابْنالزُّبَيْروَمُجَاهِدوَغَيْروَاحِدمِنْالسَّلَفوَالْخَلَف

According Sayyidna Ibn 'Abbas , Qatadah, Mujahid, Suddi, Dahhak, Kalbi and other leading commentators, the 'ten nights' refers to the [first] ten nights of Dhul Hijjah. (Summarised from Tasfeer Maariful Qur'aan & Tafseer Ibn Katheer)

Rasul-ullah (Sallaho Alaihe Wassallam) declares the good deeds of 10 days to be most Superior:

‏حدثنا‏ ‏هناد‏ ‏حدثنا‏ ‏أبومعاوية‏ ‏عن‏ ‏الأعمش‏ ‏عن‏ ‏مسلمهوالبطينوهوابنأبيعمران‏ ‏عن‏ ‏سعيدبنجبير‏ ‏عن‏ ‏ابنعباس‏ ‏قال‏ ‏قالرسولالله‏ ‏صلىاللهعليهوسلم‏ ‏مامنأيامالعملالصالحفيهنأحبإلىاللهمنهذهالأيامالعشرفقالوايارسولاللهولاالجهادفيسبيلاللهفقالرسولالله‏ ‏صلىاللهعليهوسلم‏ ‏ولاالجهادفيسبيلاللهإلارجلخرجبنفسهومالهفلميرجعمنذلكبشيء‏  ‏وفي‏ ‏الباب‏ ‏عن‏ ‏ابنعمر‏ ‏وأبيهريرة‏ ‏وعبداللهبنعمرو‏ ‏وجابر‏ ‏قال‏ ‏أبوعيسى‏ ‏حديث‏ ‏ابنعباس‏ ‏حديثحسنصحيحغريب

Narrated Ibn Abbas (RA): The Prophet said, "No good deeds done on other days are superior to those done on these (first ten days of Dhul Hijja)." Then some companions of the Prophet said, "Not even Jihad?" He replied, "Not even Jihad, except that of a man who does it by putting himself and his property in danger (for Allah's sake) and does not return with any of those things." (Reported by Tirmidhi)

Rasul-ullah (Sallaho Alaihe Wassallam) used to fast all 9 days including Arafah:

‏حدثنا‏ ‏مسدد‏ ‏حدثنا‏ ‏أبوعوانة‏ ‏عن‏ ‏الحربنالصباح‏ ‏عن‏ ‏هنيدةبنخالد‏ ‏عن‏ ‏امرأته‏ ‏عن‏ ‏بعضأزواجالنبي‏ ‏صلىاللهعليهوسلم‏ ‏قالت‏كانرسولالله‏ ‏صلىاللهعليهوسلم‏ ‏يصومتسعذيالحجةويومعاشوراءوثلاثةأياممنكلشهر

One of the wives of the Prophet (peace and blessings be upon him) said: "Allah's Messenger used to fast the [first] nine days of Dhul-Hijjah, the day of 'Ashurah, and three days of each month." (Reported by Abu Dawud).

Fasting on Arafah day is an expiation for sins committed the year before and the year after:

‏حدثنا‏ ‏أحمدبنعبدة‏ ‏أنبأنا‏ ‏حمادبنزيد‏ ‏حدثنا‏ ‏غيلانبنجرير‏ ‏عن‏ ‏عبداللهبنمعبدالزماني‏ ‏عن‏ ‏أبيقتادة‏ ‏قال‏ ‏قالرسولالله‏ ‏صلىاللهعليهوسلم‏ ‏صياميوم‏ ‏عرفة‏ ‏إني‏ ‏أحتسب‏ ‏علىاللهأنيكفرالسنةالتيقبلهوالتيبعده

Abu Qatadah (may Allah be pleased with him) is reported to have said that the Prophet (peace and blessings be upon him) said: "Fasting on the day of 'Arafah is an expiation (of sins) for two years, the year preceding it and the year following it. (Reported by Ibn Majah)

Sacrificing an animal is an established Sunnah on Eid day:

حدثنا‏ ‏حجاج‏ ‏قالحدثنا‏ ‏شعبة‏ ‏قالأخبرني‏ ‏زبيد‏ ‏قالسمعت‏ ‏الشعبي‏ ‏عن‏ ‏البراء‏ ‏قال‏ ‏سمعتالنبي‏ ‏صلىاللهعليهوسلم‏ ‏يخطبفقال‏ ‏إنأولمانبدأمنيومناهذاأننصليثمنرجعفننحرفمنفعلفقدأصابسنتنا

Narrated Al-Bara' bin 'Azib (RA) that I heard the Prophet (Sallaho Alaihe Wassallam) say when he gave a sermon (on the day of Idal-Adha), "The first thing we will do on this day of ours, is to offer the ('Id) prayer and then return to slaughter the sacrifice. Whoever does so, he acted according to our Sunna (tradition). (Reported by Bukhari)

Eating, drinking, enjoying and reciting Ayamul-Tashreeq: 11th, 12th & 13th of Dhul-Hijjah:

وَاذْكُرُوااللَّهَفِيأَيَّامٍمَعْدُودَاتٍفَمَنْتَعَجَّلَفِييَوْمَيْنِفَلَاإِثْمَعَلَيْهِوَمَنْتَأَخَّرَفَلَاإِثْمَعَلَيْهِلِمَنِاتَّقَىوَاتَّقُوااللَّهَوَاعْلَمُواأَنَّكُمْإِلَيْهِتُحْشَرُونَ

[2:203] Recite the name of Allah during the given number of days. Then whoever is early in leaving after two days, there is no sin on him, and whoever leaves later, there is no sin on him, if he is God-fearing. Fear Allah and be sure that you are going to be gathered before Him.

قَالَاِبْنعَبَّاس: الْأَيَّامالْمَعْدُودَاتأَيَّامالتَّشْرِيقوَالْأَيَّامالْمَعْلُومَاتأَيَّامالْعَشْر. وَقَالَعِكْرِمَة" وَاذْكُرُوااللَّهفِيأَيَّاممَعْدُودَات" يَعْنِيالتَّكْبِيرفِيأَيَّامالتَّشْرِيقبَعْدالصَّلَوَاتالْمَكْتُوبَات: اللَّهأَكْبَراللَّهأَكْبَر. وَقَالَالْإِمَامأَحْمَد: حَدَّثَنَاوَكِيعحَدَّثَنَامُوسَىبْنعَلِيّعَنْأَبِيهِقَالَ: سَمِعْتعُقْبَةبْنعَامِرقَالَ: قَالَرَسُولاللَّه- صَلَّىاللَّهعَلَيْهِوَسَلَّمَ- " يَوْمعَرَفَةوَيَوْمالنَّحْروَأَيَّامالتَّشْرِيقعِيدُنَاأَهْلالْإِسْلَاموَهِيَأَيَّامأَكْلٍوَشُرْبٍ

Ibn Abbas (RA) said, "The given number of days are the Ayamul-Tashreeq And the known days are the ten. Ikramah (RA) said, "Remember Allah (SWT) in the given number of days i.e. recite the Takbeer (Allahu Akbarm Allahu Akbar) in Ayamul-Tashreeq after the Fardh (obligatory) Prayers). Uqbah Ibn Amir (RA) narrates that Rasul-ullah (Sallaho Alaihe Wassallam) said that the day of Arafah, the day of Sacrifice and the Ayanul-Tashreeq are our days (for people of Islam) and eat and drink in these days. (Tafseer Ibn Katheer)

فَقَالَعُمَربْنالْخَطَّابوَعَلِيّبْنأَبِيطَالِبوَابْنعَبَّاس: ( يُكَبِّرمِنْصَلَاةالصُّبْحيَوْمعَرَفَةإِلَىالْعَصْرمِنْآخِرأَيَّامالتَّشْرِيق

Umar Ibn Khattab (RA), Ali Ibn Abi Talib (RA) & Ibn Abbas (RA) said, "Recite the Takbeer from the Fajar of the day of Arafah until the Asar of the last day of Ayamul-Tashreeq (13th of Dhul-Hijjah). (Tafseer of Imam Qurtubi)

وَفِيالْمُخْتَصَرعَنْمَالِك: اللَّهأَكْبَراللَّهأَكْبَر, لَاإِلَهإِلَّااللَّه, وَاَللَّهأَكْبَر, اللَّهأَكْبَروَلِلَّهِالْحَمْد

And in Summary it is narrated from Imam Malik (RA) [about the Takbeer] Allahu Akbar, Allahu Akbar, La Ilaha Illallah, Wallahu Akbar Allahu Akbar Wallilahil Hamd

Takbeer Tashreeq is the recitation of Allahu akbar, La ilaha illa hu Wallahu akbar, Allahu akbar wa lillahil hamd after every fardh salaah commencing from the Fajr of the 9th of Dhul Hijah until after Asr of the 13th of Dhul Hijjah. (Shami vol. 1 pg. 406)

When Ibrahim (AS) began moving the knife on his beloved son, Ismaeel (AS), the angels sent by Allah with a ram exclaimed. Allahu akbar, Allahu akbar (Allah is the greatest, Allah is the greatest). Ibrahim (AS) heard the voice of the angels and replied, La illah illa Allahu Wallahu akbar (There is no god besides Allah, and Allah is the greatest).

His son Ismaeel (AS) heard this conversation and understood that Allah had relieved him from this great rial, thus he replied, Allahu Akbar Walillahil hamd (Allah is the greatest, and to Allah belongs all praise)(Ibid).

Mustahab (Prefferable) NOT to cut any hair or trim any nails if one is preparing to make a sacrifice for Eid:

‏حدثنا‏ ‏ابنأبيعمرالمكي‏ ‏حدثنا‏ ‏سفيان‏ ‏عن‏ ‏عبدالرحمنبنحميدبنعبدالرحمنبنعوف‏ ‏سمع‏ ‏سعيدبنالمسيب‏ ‏يحدثعن‏ ‏أمسلمة‏ ‏أنالنبي‏ ‏صلىاللهعليهوسلم‏ ‏قال‏ ‏إذادخلتالعشروأرادأحدكمأنيضحيفلا‏ ‏يمس‏ ‏منشعرهوبشرهشيئا‏ ‏قيل‏ ‏لسفيان‏ ‏فإنبعضهملايرفعهقاللكنيأرفعه

Umm Salamah (May Allah be pleased with her) said: The Messenger of Allah (PBUH) said, "When anyone of you intends to sacrifice the animal and enter in the month of Dhul-Hijjah, he should not get his hair cut or nails pared till he has offered his sacrifice.'' (Reported by Muslim)

Note: Ulama have stated that this includes moustache and hair of the private parts etc. However, if the hair under the arms and in the pubic region is very long (which renders the Salaat Makrooh i.e. more than forty days), then it will become compulsory to remove such hair. However, if a person forgets to clip the nails before the 1st of Dhul Hijjah and the nails have grown so long that they may cause injury, then he may clip them.