How is the two-rak'ah prayer performed, with the recitation of Surat Al-Fath on the first night of Ramadan, to obtain the mentioned reward?

We do not know of any basis in the Sunnah for what was mentioned in the question. Therefore, it is not permissible to restrict the recitation of specific surahs to a certain time or prayer, nor to commit to reciting them daily, as all of that is an innovation (bid'ah). Innovation is the commitment to specific forms and manners, or the commitment to specific acts of worship at specific times for which such specification was not found in the Sharia. We advise you to read authentic hadith books such as "Al-Adhkar" by An-Nawawi and "Hisn Al-Muslim" by Al-Qahtani.