The second rak'ah (unit of prayer) should be performed in the same way as the first one but without the opening supplication, meaning that one should stand and begin by saying bismillaah, followed by the recitation of al-Fātihah. This is because of the following narration:
Abū Hurayrah (may Allah be pleased with him) reported that:
"When the Messenger of Allah (may the peace and blessings of Allah be upon him) stood up for the second rak'ah, he opened it with the recitation of 'al-ḥamdu-lil-laahi rab-bil 'aalameen' [The Quran: al-Fātiḥah, 1], and he did not observe [the] silence [of supplication before reciting]." [Muslim: 599]
The main difference between this rak'ah (unit of prayer) and the first is that after the second prostration and before standing up for the third rak’ah, there is a long sitting in which certain supplications are said, this is called tashahhud.
The middle tashahhud is performed after two rak'ah, for those prayers which are longer than two rak'ah in length, such as Maghrib and 'Ishā. The final tashahhud is performed at the end of all of the prayers, regardless of the length. Therefore, a prayer that is only two rak'ah has only the final tashahhud, and a prayer that is longer than two rak'ah has a middle tashahhud after two rak'ah, and a final tashahhud at the end.