Hazrat As’ad (radhiyallahu ‘anhu) selected the day of Friday as this special day for the Muslims, and on this day, he led everyone in salaah.
In short, on the basis of their own ijtihaad (understanding), the Sahaabah (radhiyallahu ‘anhum) did two things. Firstly, they established the performance of Jumu’ah, and secondly, they proposed that this auspicious day should be referred to as the day of Jumu’ah. Previously, during the times of ignorance, the day of Friday was referred to as the day of Arubah.
Allah Ta‘ala thereafter sent wahi (divine revelation) and revealed the following verses, approving of both these decisions of the Sahaabah (radhiyallahu ‘anhum):
یٰۤاَیُّہَا الَّذِیۡنَ اٰمَنُوۡۤا اِذَا نُوۡدِیَ لِلصَّلٰوۃِ مِنۡ یَّوۡمِ الۡجُمُعَۃِ فَاسۡعَوۡا اِلٰی ذِکۡرِ اللّٰہِ
“O you who believe! When the call for prayer (i.e. azaan) is proclaimed on the day of Jumu’ah, then hasten towards the zikr of Allah…” (Surah Jumu’ah v. 9)
Besides establishing the compulsion of Jumu’ah, this verse also proves that Allah Ta‘ala approved the name Jumu’ah for this day. The divine revelation of Allah Ta‘ala did not use the name Yawm-e-Arubah (day of Arubah) for Friday, as was prevalent in the pre-Islamic days of ignorance, and instead used exactly the same name chosen by the Ansaar. Judging from this perspective, Allah Ta‘ala had endorsed and approved of the ijtihaad (understanding) of the Ansaar.
Merely a few days later, the letter of Rasulullah (sallallahu ‘alaihi wasallam), addressed to Hazrat Mus’ab bin Umair (radhiyallahu ‘anhu), reached the people of Madinah Munawwarah. In this letter, Rasulullah (sallallahu ‘alaihi wasallam) instructed the people of Madinah Munawwarah to congregate after midday on the day of Jumu’ah and perform two rakaats of salaah.
Hazrat Abdur Rahmaan bin Ka’b bin Maalik (radhiyallahu ‘anhu) says, “Whenever my father, Hazrat Ka’b bin Maalik (radhiyallahu ‘anhu), would hear the azaan of Jumuah being called out, he would think of Hazrat As’ad bin Zuraarah (radhiyallahu ‘anhu) and make dua of forgiveness for him. When I once asked him the reason for this, he replied, ‘In Madinah, he was the first person to lead us in Jumu’ah Salaah.’”
(Extracted from Seeratul Mustafa 1/336-337)