Well, let’s start with Lent, the forty days preceding Easter, which are meant to be a time of introspection and reflection. The model for Lent is the Temptation of Christ in the Wilderness, which lasted for forty days, and is recorded in the three synoptic Gospels: Matthew 4:1-11, Mark 1:12-13, and Luke 4:1-13. Lent is one way for believers to try to share in that experience.
Turning to Holy Week, it starts with Palm Sunday. That day is to commemorate the entry of Christ into Jerusalam, being greeted by crowds waving palm branches and crying “hosanna”. In churches that observe Palm Sunday, palms are handed out to the congregation, hymns often echo the “hosanna” theme, and there is sometimes a procession through the church, to represent the original procession. The basis for these commemorations are: Matthew 21: 1-11, Mark 11:1-11, Luke 19:28-44, and John 12: 12-19.
Thursday of Holy Week, called Maundy Thursday in some traditions, is the source of three traditions. First, there is Jesus’ Washing of the Feet of the Disciples, as recorded by John 13:1-15. That practice is most famously continued by the Pope himself on Maundy Thursday, but is also followed by many other denominations, as noted in the Wiki article.
Then, and even more importantly, is the Institution of the Last Supper (or Mass, or Eucharist, or Communion, depending on the terminology of each denomination). This, along with baptism, is one of the central sacraments of Christian theology. The Synoptic Gospels and Paul’s Epistle to the Corinthians contain jesus’s explicit instructions to continue the practice of the Last Supper, “in remembrance of me.” (See: Matthew 26:26-29, Mark 14:22-25, Luke 22:13-20, 1 Corinthians 11:23-26.)
Third, after the Supper, Jesus and his disciples sang a hymn (Matthew 26:30, Mark 14:26). This is of course now an almost universal practice among Christian churches, not just on Easter. (See this recent thread on the topic: Music or Easter services?
Then comes Good Friday, commemorating the trial, cruxifixion and death of Jesus, as recorded in all four Gospels. Services on this day are sombre, as befitting the events it commemorates. Customarily the priest wears a black cassock, there is little or no singing, the altar is swept bare, and the cross is covered in a black veil as a sign of mourning. There is no eucharist, since this is a day of mourning, not a day of celebration.
Finally, on Sunday, it is Easter itself, to celebrate the Resurrection, which is recorded in all four Gospels: Matthew 28, Mark 16, Luke 24, and John 20. The church services are joyful, with lots of hymns of praise, and the celebration of the Eucharist - probably the most holy observance of the church, since it celebrates both the institution of the eucharist, as a reminder of salvation, and the resurrection of Christ on Easter Sunday.
So yes, the Easter rituals of the church are firmly grounded in the Bible.