What is the Sunnah prayer after the Friday Prayer? How should it be performed?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

The voluntary prayer after the Friday Prayer is reported to be two Rak‘ahs. Ibn ‘Umar said that the Prophet, sallallaahu ‘alayhi wa sallam, used to perform two Rak‘ahs in his house on Friday. [Al-Bukhari and Muslim] Another tradition stated that the Sunnah prayer for it is four Rak‘ahs. Abu Hurayrah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever is to pray (Sunnah) after the Friday Prayer should pray four Rak‘ahs." [Muslim]

Hence, one can perform two Rak‘ahs after the prayer and it is even better to perform four Rak‘ahs. Shaykhul-Islam Ibn Taymiyyah combined between the two previous narrations as he said, "If one performs voluntary prayers after the Friday prayer in the mosque, let him perform four Rak‘ahs and, if he performs them in his house, let him perform two Rak‘ahs." This is a good and harmonious combination between the two previously mentioned Hadeeths.