Whoever omits the opening takbeer, his prayer does not count
Question

When should the opening takbeer (takbeerat al-ihram) be said? What is the ruling on the prayer of one who does not say it because of ignorance on his part and does not omit it deliberately? What does he have to do?.
Praise be to Allah.The opening takbeer is one of the pillars or essential parts of the prayer, without which a person’s prayer is invalid and he has not entered the prayer if he does not say it. The Prophet (peace and blessings of Allah be upon him) said: “No person’s prayer is complete unless he does wudoo’ as it should be done and then says ‘Allahu akbar.’” Al-Albaani said: It was narrated by al-Tabaraani with a saheeh isnaad.  Ibn Qudaamah said: This is the view of the majority of scholars, past and present. 
Al-Mughni, 2/126; see also al-Majmoo’, 3/175. 
This is the first thing with which a person should start his prayer, because the Prophet (peace and blessings of Allah be upon him) said: “The key to prayer is purification, its opening is to say Allahu akbar and its closing is to say al-salaamu’ alaykum.”  Narrated by Ahmad, 1009; Abu Dawood, 618; al-Tirmidhi, 238; Ibn Maajah, 276. al-Nawawi said: its isnaad is saheeh. 
The phrase tahreemuha al-takbeer (translated here as “its opening is to say Allahu akbar”) means that this takbeer makes it haraam for the worshipper to eat, drink or do other things that are permissible outside of the prayer, or that one enters into the sanctity (hurmah) of the prayer by saying the takbeer. See al-Majmoo’, ‘Awn al-Ma’bood. 
With regard to when the opening takbeer should be said, it is the first thing that the person does in the prayer, so he should say it when he stands to pray; he should turn to face the qiblah and then say the takbeer, then recite the opening du’aa’, then seek refuge with Allah from the accursed Shaytaan, then start reciting Soorat al-Fatihah. 
It is mustahabb to raise the hands when saying this takbeer, raising them until they are level with the shoulders. This raising of the hands is a confirmed Sunnah (Sunnah mu’akkadah). See Sifat Salaat al-Nabi (peace and blessings of Allah be upon him) by al-Albaani [Available in English under the title The Prophet’s Prayer Described]. 
As the opening takbeer is a pillar or essential part of the prayer, if a person omits it, deliberately or by mistake, his prayer does not count, i.e., it does not come under the rulings on prayer. See al-Mughni, 2/128. 
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: If a person omits the opening takbeer by mistake, what is the ruling? 
He replied: If a worshipper omits the opening takbeer, by mistake or deliberately, his prayer does not count, because the prayer cannot begin without the opening takbeer. If we assume that a person stands in the row then starts with the opening du’aa’ and recitation of al-Fatihah, and he continues with the prayer, we say that has not entered prayer in the first place, even if he performs all the rak’ahs. Fataawa al-Shaykh, 14/36. 
With regard to the one who omits it and starts to pray because he is unaware that it is obligatory, if the time for the prayer in which he started to pray without the opening takbeer has not yet ended, then he has to repeat the prayer, as the Prophet (peace and blessings of Allah be upon him) commanded the Sahaabi who was not at ease in his prayer and did not pray properly to repeat the prayer in front of him and he told him: “Go back and pray, for you have not prayed.” (Agreed upon).  
But if the time of the prayer which he prayed without the opening takbeer out of ignorance has ended, then he should try to do what is on the safe side, and repeat this prayer. Similarly if he had offered more than one prayer in this fashion, he should do what is on the safe side and make sure he has discharged his duty. That is because the basic principle according to the majority of scholars is that if a person omits a duty out of ignorance or forgetfulness, he has not discharged his duty until he does it. See al-Qawaa’id wa’l-Usool al-Jaami’ah by Ibn Sa’di, p. 78 
And the opening takbeer is one of the duties that are enjoined upon the one who prays.  
It is very unlikely that the one who was praying would do this, especially if he was living in a Muslim land. It is very unlikely that he would be unaware of such rulings. At the very least he would see the Muslims around him doing that and would do the same as they do, or at least he would ask about what they are doing.  
And Allah is the source of strength.