The Prophet ﷺ taught Muslims how to answer the muezzin, what to say after the adhan, and to make du'a before the iqamah. These entries put the sequence in order. After answering the muezzin, send blessings on the Prophet ﷺ, for Allah (SWT) sends ten blessings on the one who sends one (Sahih Muslim 384).
Idha sami'tumu-n-nida'a, faqulu mithla ma yaqulu-l-mu'adhdhin.
“When you hear the call to prayer, say what the muezzin says.”
Echo each phrase of the adhan after the muezzin, phrase by phrase. The two hayya phrases are the one exception, they have their own response.
La hawla wa la quwwata illa billah.
“There is no power and no strength except with Allah.”
When the muezzin calls 'come to prayer' and 'come to success', respond with these words instead of repeating the call.
Wa ana ashhadu an la ilaha illallahu wahdahu la shareeka lah, wa anna Muhammadan 'abduhu wa rasuluh. Radeetu billahi rabban, wa bi-Muhammadin rasulan, wa bil-islami deena.
“And I too bear witness that there is no god but Allah alone, with no partner, and that Muhammad ﷺ is His servant and His Messenger. I am pleased with Allah as Lord, with Muhammad ﷺ as Messenger, and with Islam as religion.”
Said when the muezzin pronounces the shahada. The Prophet ﷺ promised that whoever says this from his heart, his sins are forgiven.
Allahumma salli 'ala Muhammad.
“O Allah, send Your blessings upon Muhammad ﷺ.”
After answering the muezzin, send salawat on the Prophet ﷺ. Whoever sends one salawat upon him, Allah (SWT) sends ten upon him in return.
Allahumma rabba hadhihi-d-da'wati-t-tammah, wa-s-salati-l-qa'imah, ati Muhammadani-l-waseelata wa-l-fadeelah, wab'ath-hu maqaman mahmudani-lladhi wa'adtah.
“O Allah, Lord of this perfect call and of the prayer about to be established, grant Muhammad ﷺ al-Waseelah and the highest honour, and raise him to the praised station You have promised him.”
The Prophet ﷺ said that whoever says this after hearing the adhan, his intercession becomes due for him on the Day of Resurrection.
Ad-du'a'u la yuraddu bayna-l-adhani wa-l-iqamah.
“The supplication made between the adhan and the iqamah is not rejected.”
Not a fixed wording but an open door. In the quiet minutes before the iqamah, ask Allah (SWT) for whatever you need, in any words.