One way to answer the Adhaan is described here. There’s another way according to the Sunnah. It’s more or less the same as the previous one, just a slight change in the answer..
Narrated Abu Umama bin Sahl bin Hunaif:
I heard Muawiya bin Abi Sufyan (repeating the statements of the Adhan) while he was sitting on the pulpit. When the Muadh-dhin pronounced the Adhan saying, “Allahu-Akbar, Allahu Akbar”, Muawiya said: “Allah Akbar, Allahu Akbar.” And when the Muadh-dhin said, “Ash-hadu an la ilaha illal-lah (I testify that none has the right to be worshipped but Allah)”, Muawiya said, “And (so do) I”. When he said, “Ash-hadu anna Muhammadan Rasulullah” (I testify that Muhammad is Allah’s Apostle), Muawiya said, “And (so do) I”. When the Adhan was finished, Muawiya said, “O people, when the Muadh-dhin pronounced the Adhan I heard Allah’s Apostle on this very pulpit saying what you have just heard me saying”.
“And (so do) I” is wa ‘ana (وأنا) in Arabic. Cool, eh? ;)
Narrated Abu Said Al-Khudri:
Allah’s Apostle said, “Whenever you hear the Adhan, say what the Mu’adhdhin is saying.
Narrated ‘Isa bin Talha:
that he had heard Mu’awiya repeating the words of Adhan up to “Wa ash-hadu Anna Muhammadan Rasulul-lah (and I testify that Muhammad is Allah’s Apostle.)”
Narrated Yahya as above (586) and added:
“Some of my companions told me that Hisham had said, “When the Muadhin said, “Haiya alas-sala(t) (come for the prayer).” Muawiya said, “La hawla wala quwata illa billah (There is neither might nor any power except with Allah)” and added, “We heard your Prophet saying the same.”
So, when the muadhin (caller to prayer) is pronouncing the Adhaan, you’re supposed to repeat what he says. But when he says ‘hayya alas-salah‘ and ‘hayya alal-falah‘, say: ‘la hawla wala quwwata illa billah‘.