The Shulchan Aruch writes (109:2; listen to audio for precise citation) that if a person comes late to the synagogues and misses the congregation's silent Amidah, he can still earn the merit of praying with the congregation by reciting the Amidah word for word with the Chazan. When he and the Chazan complete the Beracha of "Mechayei Ha'meitim," he recites Kedusha together with the Chazan. He then continues "Ata Kadosh" with the Chazan, and bows with the Chazan at the recitation of "Modim." After the Beracha of "Ha'tov Shimcha U'le'cha Na'eh Le'hodot," he should stop and listen to Birkat Kohanim. He may also answer "Amen" to the Beracha preceding Birkat Kohanim and after each of the three verses of Birkat Kohanim (after "Ve'yishmirecha," "Vi'chuneka" and "Shalom"). He should not, however, answer "Baruch Hu U'varuch Shemo" during Birkat Kohanim.
If a person recites the silent Amidah and, as he completes the Beracha of "Mechayei Ha'meitim," he hears a congregation in a different Minyan reciting Kedusha, he should recite Kedusha together with them. Even though he is not participating in that Minyan, he should nevertheless join them for the recitation of Kedusha, since he has reached the point in the Amidah where Kedusha is inserted. (This occasionally happens in "Shteibels," where several Minyanim pray in the same area, or at the Western Wall, where many Minyanim pray at the same time.) He does not, however, interrupt his Amidah to join a congregation reciting "Kadosh Kadosh" of Yotzer (the section before Shema) or of "U'va Le'tziyon." Only if one hears the recitation of Kedusha as part of a Chazan's repetition does he join in the recitation if he had just completed "Mechayei Ha'meitim."
This Halacha applies only to a person praying Shacharit or Mincha. If a person recites Arvit early, before sundown (as many people do on Erev Shabbat during the summer months), and, as he completes the Beracha of "Mechayei Ha'meitim," he hears a congregation reciting Kedusha of Mincha, he does not recite Kedusha along with them. Since he currently recites Arvit, during which Kedusha is not recited, he should not interrupt his Amidah to recite Kedusha.
Similarly, if a person completes "Mechayei Ha'meitim" in the Amidah of Shacharit or Mincha, and he hears a different Minyan reciting the Kedusha of "Keter" in Musaf, he does not join them in the recitation of Kedusha. Since that Minyan recites a Kedusha that is relevant only to Musaf, and this individual is reciting a different prayer, he does not join them in the recitation of "Keter." (Ashkenazim, who recite the Kedusha of "Nakdishach" during Musaf, would join the Kedusha recitation in such a case.)
Summary: One who comes late to the synagogue and misses the congregation's silent Amidah should recite the Amidah word for word together with the Chazan as he repeats the Amidah, and he may recite Kedusha together with the Chazan, as well. If somebody reciting the Amidah of Shacharit or Mincha hears a different Minyan reciting "Kedusha" as he completes the Beracha of "Mechayei Ha'meitim," he joins them in reciting Kedusha. This applies only if they recite the Kedusha of the Chazan's repetition of the Amidah, and not the other recitations of "Kadosh Kadosh," and that they are not reciting the Kedusha of "Keter."
(Based on Shulchan Aruch 109:1-3, and Halacha Berura vol. 6, pp. 84-90)
