Allah the Most High says in the Quran:
‘O you who have believed, when [the adhan] is called for the prayer on the day of Jumu'ah [Friday], then proceed to the remembrance of Allah and leave trade. That is better for you, if you only knew.’ [62:9]
The prophet Muhammad ﷺ said:
The best day on which the sun has risen is Friday. It was on this day that Adam was created, on it he was made to enter Paradise, and on it he was removed from it. And the last hour will take place on no day other than Friday. [Muslim]
The Friday prayer is a congregational prayer consisting of two raka'at that is performed in the place of Dhuhr. We pray it behind an imam at a mosque, local community center, or some other place of gathering.
In addition to prayer, there is a khutbah (sermon) is delivered right before the fard prayer. There are also sunnah prayers one can do before the khutbah (4 raka'at), and after the fard prayer (4 raka'at).
Attending the Friday prayer is obligatory for everyone who meets these conditions:
Being a male person who reached puberty;
Not travelling;
Having sound health (i.e. not being too sick, blind, or unable to walk);
Having safety of passage.
Those, who do not meet any of these conditions can choose to either pray dhuhr as usual or attend the Friday prayer. If one missed the Friday prayer due to a circumstance, then the Dhuhr is prayed in its stead.
Khutbah is the speech or sermon delivered right before the prayer. It is obligatory (wajib) for the attendees to listen and not speak.
The Messenger of Allah (may Allah bless him and give him peace) said,
"If anyone performs Wudu' properly, then comes to the Friday prayer, listens to the Khutbah (religious talk) attentively and keeps silent, his (minor) sins between that Friday and the following Friday will be forgiven, with the addition of three more days; but he who touches pebbles has caused an interruption. "
The Messenger of Allah (ﷺ) has also said:
“If you say to your companion on the day of Jumu’ah, while the Imam is delivering the sermon, ‘Be quiet’ — you have rendered your reward void.” [Bukhari]
Therefore, while the khutbah is delivered, we do not greet people, and when wanting to say "aameen" to a dua or to send blessings upon the Prophet (ﷺ) , we say it silently in the heart. Being quiet also includes paying full attention and not looking at your phone, since we see many people using their phones during khutbah.
There are many sunnahs (recommended actions) of Friday we can do:
Perform ghusl;
Brush the teeth, cut the nails, and trim the mustache;
Wear your best clothes, use misk (the good scent), and going to the mosque early and on foot;
Say salawat (blessings for the Prophet), for example: Allahumma salli wa sallim عalaa nabiyyinaa Muhammad (O Allah, bless and grant peace to our prophet Muhammad);
Read Surah “Al-Kahf” (chapter 18 of the Qur'an);
Make more duas between Asr and Maghrib.
More generally, we should increase our good deeds on Fridays, as it is the best of the days on which reward is greater, and every good action draws us closer to Allah. May Allah bless the Fridays for us and accept from us. Aameen!