While the Shofar (ram's horn) is being blown, what should a person be doing or thinking while the mitzvah (commandment) is happening? They shouldn't be doing anything else. The person should only be focusing and concentrating on the mitzvah. They should think to themselves, “We're performing a mitzvah from the Torah to hear the sounds of the Shofar.” The person should make sure to answer Amen (so be it) to the Beracha (blessing), and not say Baruch Hu u'varuch shemo (Blessed is He and blessed is His name), so as not to create an interruption in the Beracha. And the person should be having in mind that the blower is fulfilling their obligation, as well the Chazan (cantor) has in mind to fulfill the obligation of the Kahal (congregation).
Many people have the custom, based on the Arizal, to recite Vidui, to recite words of confession, while the Tekiot (shofar blasts) are going on. Hacham Ovadia is against this practice. He says that it could constitute a Hefsek (interruption). Although those who are Mekubalim (Kabbalists) might follow the Ari, he says it's preferable for a person not to recite Vidui during the Kolot (sounds). Rather, they should be focused on the sounds themselves, thinking about Akedat Yitzchak and all of the different reasons why we blow the Shofar. If they want to think thoughts of Teshuvah, thoughts of commitment, or repent in their minds, they may do so. However, they should not say anything, so as not to create a Hefsek during the sounds of the Shofar. Have a great day.