The eclipse Prayer is sunnah to do. You may pray it like any two rak^ah prayer. However there is a complete sunnah way and a minimum complete sunnah way.
The complete sunnah way is to have two standings and two bowings in each cycle and to recite the chapter of al-Baqarah or its equivalent amount in the first standing and the equivalent of 100 verses from al-Baqarah in the second standing.
In the second rak^ah for the first standing you recite the equivalent of 150 verses of al-Baqarah and for the second standing the equivalent of 80 verses from al-Baqarah. In the first rak^ah for the first bowing you say tasbeeH like the length of 100 verses from al baqarah and in the second like 80 verses. In the second rak^ah in the first bowing like 70 verses and in the second bowing like 50 verses. it is sunnah to give two speeches like the ^eid except without saying Allāhu Akbar.
صلاة الكسوف والخسوف
وصلاة الكسوف سنة مؤكدة فإن فاتت لم تقض ويصلي لكسوف الشمس وخسوف القمر ركعتين في كل ركعة قيامان يطيل القراءة فيهما وركوعان يطيل التسبيح فيهما دون السجود ويخطب بعدها خطبتين ويسر في كسوف الشمس ويجهر في خسوف القمر.