Concerning the athan (the call to prayer)

يقول مثل ما يقول المؤذن إلا في (حي على الصلاة ، وحي على الفلاح) فيقول لا حول ولا قوة إلا بالله.

Repeat what the Mu'adh-dhin says, except for when he says: Hayya 'alas-Salāh (hasten to the prayer) and Hayya 'alal-Falāh (hasten to salvation). Here you should say: Lā ḥawla wa lā quwwata 'illā billāh. There is no might and no power except by Allah. Reference: Al-Bukhari 1/152, Muslim 1/288.

Reference : Hisn al-Muslim 22

وَأَنا أَشْـهَدُ أَنْ لا إِلـهَ إِلاّ اللهُ وَحْـدَهُ لا شَـريكَ لَـه ، وَأَنَّ محَمّـداً عَبْـدُهُ وَرَسـولُه، رَضيـتُ بِاللهِ رَبَّاً ، وَبِمُحَمَّـدٍ رَسـولاً وَبِالإِسْلامِ دينَـاً

Wa 'anā 'ash-hadu 'an lā 'ilāha 'illallāhu waḥdahu lā sharīka lahu wa 'anna Muḥammadan 'abduhu wa rasūluhu, raḍītu billāhi rabban, wa bi Muḥammadin rasūlan wa bi 'l-islāmi dīnan. I bear witness that none has the right to be worshipped but Allah alone, Who has no partner, and that Muhammad is His slave and His Messenger. I am pleased with Allah as my Lord, with Muhammad as my Messenger and with Islam as my religion.1 [To be recited in Arabic after the mu'adh-dhin's tashahhud or the words of affirmation of Faith] 2 Reference: 1. Muslim 1/290. 2. Ibn Khuzaymah 1/220.

Reference : Hisn al-Muslim 23

يُصَلِّي عَلَى النَّبِيِّ صلى الله عليه وسلم بَعْدَ فَرَاغِهِ مِنْ إِجَابَةِ الْمُؤَذِّنِ

After replying to the call of Mu'adh-dhin. you should recite in Arabic Allah's blessings on the Prophet (ﷺ). Reference: Muslim 1/288

Reference : Hisn al-Muslim 24

اللّهُـمَّ رَبَّ هَذِهِ الدّعْـوَةِ التّـامَّة وَالصّلاةِ القَـائِمَة آتِ محَـمَّداً الوَسيـلةَ وَالْفَضـيلَة وَابْعَـثْه مَقـامـاً مَحـموداً الَّذي وَعَـدْتَه [إِنَّـكَ لا تُـخْلِفُ الميـعاد]

Allāhumma rabba hādhihi 'd-da'wati 't-tāmmah waṣ-ṣalāti 'l-qā'imah, 'āti Muhammadani 'l-wasīlata walfaḍīlata, wab 'ath-hu maqāma 'm-mahmūdani 'l-ladhī wa`adtahu, ['innaka lā tukhliful-mī'ād] O Allah , Lord of this perfect call and established prayer. Grant Muhammad the intercession and favor, and raise him to the honored station You have promised him, [verily You do not neglect promises]. Reference: Al-Bukhari 1/152, and the addition between brackets is from Al-Bayhaqi 1/410 with a good (Hasan) chain of narration. See 'Abdul-Azlz bin Baz's Tuhfatul-'Akhyar, pg. 38.

Reference : Hisn al-Muslim 25

يَدْعُو لِنَفسِهِ بَيْنَ الْأَذَانِ وَالْإِقَامَةِ فَإِنَّ الدُّعَاءَ حِينَئِذٍ لاَ يُرَدُّ

Between the call to prayer and the 'Iqamah, you should supplicate Allah for yourself. Invocation during this time is not rejected. Reference: At-Tirmidhi, Abu Dawud, Ahmed. See Irwaa Al-Ghalil 1/262

Reference : Hisn al-Muslim 26