This day is a very special day for Muslim just like Saturday and Sunday are special to the Jews and Christians respectively.
Although, Friday according to Prophet Muhammad is a festive day, but it isn't the day to dance all day and forget the purpose of our creation.
Jumuah day (day of gathering) is that day Muslims gather for the purpose of remembering, praising and worshipping Allah. Hence, we are encouraged to do our best to make supplications during the last hours of Friday.
A number of ahadeeth of the prophet tell us about the special moment to pray to Allah on Friday.
Abu Sa'id and Abu Hurairah report that the Messenger of Allah said: "On Jumu'ah there is a time that if a believing slave asks Allah during it for some good,[Allah will definitely] give it to him, and that time is after the 'asr salah." This is related by Ahmad. Al-'Iraqi calls it sahih.
Jabir reports that the Messenger of Allah said: "The day of Jumu'ah has twelve hours, and during one of the hours, you will not find a Muslim slave[of Allah] asking Allah for something ,but that He will give it to him. Seek it in the last hour after the 'Asr salah." This is related by anNasa'i, Abu Dawud, and by alHakim in al-Mustadrak, and he calls it sahih according to Muslim's criteria. Ibn Hajar says that its chain is hasan.
Abu Salamah ibn'Abdurrahman reports that some companions of the Prophet gathered and mentioned the "hour on Jumu'ah." They left and did not differ on the fact that it is the last hour of Jumu'ah. This is related by Sa'id ibnMansur in his Sunan and al-Hafiz Ibn Hajar calls it sahih.
All these ahadeeth talk about the virtues of Friday and the right time to make supplications to Allah today. Do not forget it is the hour between the end of Asr prayer and before Maghrib prayer. You can read Suratul-Kahf at this time.