Jesus was put on the Cross at the very end of the third hour (the time between 9 and noon), and almost the sixth hour. He died at the ninth hour:
Mark 15:25, 33
And it was the third hour, and they crucified Him... And when the sixth hour was come, there was darkness over the whole earth until the ninth hour.
Because Jesus was on the Cross between the hours of Noon and 3:00 PM, these three hours today are considered the most sacred of all. A devotion called "Tre Ore" or "Three Hours' Agony" might be held at this time; if not, you can do it yourself by meditating on His Passion -- reading the Gospel narratives of the Passion, making the Stations of the Cross by yourself, praying the Sorrowful Mysteries of the Rosary, praying the Litany of the Passion, etc. Draw the curtains, take the phone off the hook, turn off televisions and radios, quiet your environment and yourself, and meditate on what Christ has done for you. At 3:00, "The Hour" He died, the atmosphere should be as if you are standing next to the deathbed of your father who died a moment ago.
Catholics also focus their attention on Mary this day and tomorrow (Holy Saturday), empathizing with the pain she endured as Our Lady of Sorrows. In another break in the tradition of veiling statues since Passion Sunday, they might dress the image of Our Lady in a black dress or veil, placing flowers of mourning before it in her honor.
Though a somber atmosphere will last until the Easter Vigil, after "The Hour" (3:00 PM) passes, it eases a bit, and life can go back to a "somber normal." The phone can put back on the hook, etc., but candles and other symbols of Christ shouldn't be used, music shouldn't be played, raucous games should be eliminated, etc., while Christ is "in His Tomb" -- i.e., until after Vigil of Holy Saturday when Eastertide officially begins.
No true Mass is offered today (or tomorrow until the Vigil tomorrow evening); instead a liturgy called the "Mass of the Presanctified" is offered, which is not a true Mass because no consecration takes place. Instead, we consume Hosts consecrated at yesterday's Mass. Vestment colors will be black, and the liturgy consists of lessons, prayer, St. John's version of the Passion, and ends with a long series of prayers for various intentions: the Church, the Pope, the faithful, those engaged in public affairs, catechumens, the needs of the faithful, unity, the conversion of the Jews, the conversion of infidels. These intentions are called the Great Intercessions, and we kneel after each.
Then the Cross will be unveiled and and elevated to be adored by our kneeling three times before it at the words "Venite, adorémus" (come, let us adore). We kneel thrice because He was mocked thrice: in the high priest's courtyard, in Pilate's house, and on Mt. Calvary. Then the priest lays the Cross on a cushion and covers it with a white veil to symbolize the Entombment. He takes off his shoes, like Moses before God, and kneels three times as the choir chants. He and his acolytes kneel and kiss the Cross.
The Cross is held up for us, and we file past - - men first, then women -- to kneel and kiss the Cross while the choir sings the Improperia (the Reproaches) of Christ, in which Our Lord reminds us all He has done for us and our ingratitude towards Him. Note the use of the singular "thee" in these Reproaches. Our Lord is speaking to you. The first three of the twelve Reproaches are:
O My people, wha have I done to thee? Or wherein have I afflicted thee? Answer Me. Because I led thee out of the land of Egypt, thou hast prepared a Cross for thy Savior.
Because I led thee out through the desert forty years: and fed thee with manna, and brought thee into a land exceeding good, thou has prepared a Cross for thy Savior.
What more ought I to have done for thee, that I have not done? I planted thee, indeed, My most beautiful vineyard: and thou has become exceeding bitter to Me: for in My thirst thou gavest Me vinegar to drink, and with a lance thou hast pierced the side of thy Savior.
A second choir responds to each of those Reproaches with a trisagion in Greek and Latin. You might recognize its English translation if you've ever prayed the Divine Mercy chaplet:
O holy God!
O holy God!
O holy strong One!
O holy strong One!
O holy immortal One, have mercy on us.
O holy immortal One, have mercy on us!
The remaining nine Reproaches are answered with the response "O my people, what have I done to thee? or wherein have I afflicted thee? Answer me." ("Popule meus, quid feci tibi? Aut in quo constristavi te? Responde mihi."). The words evoke awe in reminding us of our ancient Israelite heritage -- and evoke humility in recalling how our ancestors failed repeatedly:
For thy sake I scourged Egypt with its first-born: and thou didst deliver Me up to be scourged.
I led thee out of Egypt having drowned Pharao in the Red Sea: and thou to the chief priests didst deliver Me.
I opened the sea before thee: and thou with a spear didst open My side.
I went before thee in a pillar of cloud: and thou didst lead Me to the judgment hall of Pilate.
I fed thee with manna in the desert; and thou didst beat Me with blows and scourges.
I gave thee the water of salvation from the rock to drink: and thou didst give Me gall and vinegar.
For thy sake I struck the kings of the Chanaanites: and thou didst strike My head with a reed.
I gave thee a royal scepter: and thou didst give My head a crown of thorns.
I exalted thee with great strength: and thou didst hang Me on the gibbet of the Cross.
After the Reproaches, we receive Communion, receiving Hosts consecrated at yesterday's Mass.
It is customary for churches to offer the Way of the Cross devotion on this day, especially around 3:00, the hour of His death. And, again, there may be a tenebrae service (consisting of the Matins and Lauds for Holy Saturday).
Our Lord was laid in the tomb owned by St. Joseph of Arimethea, at a site over which stands now the Basilica of the Holy Sepulchre, first built on the spot by St. Helena, mother of Constantine the Great. In Jesus's time, the tomb was outside the city; by the time St. Helena was told of it, it was inside the city walls because Hadrian expanded the city's perimeter -- and had built a pagan temple over the site. The basilica built by St. Helena was destroyed by Caliph al-Hakim in A.D. 1009, and was later re-built over time.
The exact spot where "the New Adam" was crucified is marked inside the Basilica, and is said to stand over the place where the first Adam was buried. Matthew tells us what happened when Our Lord's Soul left His Body:
And behold the veil of the temple was rent in two from the top even to the bottom, and the earth quaked, and the rocks were rent.
Tradition tells us that among those rocks which were rent were those beneath the Cross, and that His Blood dripped down into the crevices (visible today) and reached the spot where the first Adam was interred. The Blood of the New Adam covers the sins of the first Adam!