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.
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.
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
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.
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