The Gemara in Masechet Berachot (21) discusses the common case of a person who arrives in the synagogue late, after the congregation has begun reciting the Amida. In such a case, the Gemara writes, the person must make an assessment whether he would be able to complete the Amida by the time the Hazan reaches Nakdishach. If he feels that he can complete the Amida in time for Nakdishach, then he should begin the Amida and then, assuming he finishes in time, answer to Nakdishach together with the congregation. If he feels that he will be unable to recite the entire Amida by the time the Hazan reaches Nakdishach, then he should not begin the Amida. Instead, he should wait for the Hazan to recite Nakdishach so he can respond together with the congregation.
The Shulhan Aruch codifies this Halacha in Orah Haim (109). He adds that if the person waited until after Nakdishach, he should not begin the Amida immediately at that point unless he feels he can reach Modim together with the Hazan. If he suspects that he would be unable to reach Modim with the Hazan – because the Hazan has already finished the first three Berachot of the Amida – then he should wait until the Hazan reaches Modim, so he can bow and recite Modim together with the congregation. In such a case, he does not begin the Amida until after Modim. However, if he feels he can catch up to the Hazan by Modim, then he should begin the Amida immediately after Nakdishach.
This entire discussion relates to a situation of a person who arrives late in the synagogue; it does not apply to a case of one who started the Amida together with the congregation but recites the Amida at a slower pace and thus suspects that he will miss Nakdishach. Strictly speaking, a person who knows he prays more slowly than the congregation and will likely miss Nakdishach may nevertheless begin the Amida together with the congregation and proceed at his usual pace. However, Hacham Ovadia Yosef, in his Yabia Omer, writes that it is preferable for such a person to begin the Amida before the congregation begins. During Shaharit, for example, he should begin while the congregation recites Emet Ve’yasiv or Ezrat Abotenu. He is still considered as praying Tefila Be’sibur (the communal prayer), despite having begun his prayer a few moments before the congregation. This way, he will be able to complete his prayer in time to answer to Nakdishach.
Summary: A person who arrived late in the synagogue, after the congregation has begun the Amida, should begin the Amida at that point only if he feels he can complete the Amida in time for Nakdishach. Otherwise, he must wait until after Nakdishach. A person who knows he prays more slowly than the congregation and suspects he will miss Nakdishach should preferably begin the Amida before the congregation, so he can finish the Amida in time for Nakdishach.
