Concerning the athan (the call to prayer)

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.

[ Al-Bukhari 1/152, Muslim 1/288. Hisn al-Muslim 22 ]

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

[ 1. Muslim 1/290. 2. Ibn Khuzaymah 1/220. Hisn al-Muslim 23 ]

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

[ Muslim 1/288. Hisn al-Muslim 24 ]

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].

[ 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. Hisn al-Muslim 25 ]

Between the call to prayer and the 'Iqamah, you should supplicate Allah for yourself. Invocation during this time is not rejected.

[ At-Tirmidhi, Abu Dawud, Ahmed. See Irwaa Al-Ghalil 1/262. Hisn al-Muslim 26 ]