It is too late to mark the start of a new liturgical year; that began with the first Sunday of Advent, on Dec. 1. But you have already experienced the change at Mass: The church is now in Year A of its three-year cyclical lectionary, which means that readings are built around the Gospel of Matthew (with Mark and Luke to follow in subsequent years).
As for the secular world, Jan. 1 marks a new year that is the last in the four-year cycle of U.S. presidential politics; 2020 also brings a Summer Olympics and multiple commemorations of the 75th anniversary of the close of World War II.
Celebrations of the liturgical year 2020
Jan. 1: Solemnity of Mary*
Jan. 5: Solemnity of the Epiphany of the Lord
Jan. 12: The Baptism of the Lord
Feb. 26: Ash Wednesday
March 19: Solemnity of Saint Joseph, Spouse of the Blessed Virgin Mary
March 25: Solemnity of the Annunciation of the Lord
April 5: Palm Sunday of the Passion of the Lord
April 10: Good Friday
April 12: Easter Sunday
April 19: Divine Mercy Sunday
May 21: The Ascension of the Lord (Thursday)*
May 31: Pentecost Sunday
June 7: Solemnity of the Most Holy Trinity
June 14: The Most Holy Body and Blood of Christ (Corpus Christi)
June 19: Solemnity of the Most Sacred Heart of Jesus
June 24: Solemnity of the Nativity of Saint John the Baptist
June 29: Solemnity of Saints Peter and Paul, Apostles
Aug. 15: Solemnity of the Assumption of the Blessed Virgin Mary**
Nov. 1: Solemnity of All Saints**
Nov. 2: The Commemoration of All the Faithful Departed (All Souls Day)
Nov. 22: Solemnity of Our Lord Jesus Christ, King of the Universe (Christ the King)
Nov. 29: First Sunday of Advent
Dec. 8: Solemnity of the Immaculate Conception of the Blessed Virgin Mary*
Dec. 25: The Nativity of the Lord (Christmas)*
*Holy Day of Obligation
**Not a separate Holy Day of Obligation in 2020 because it falls on a Saturday or Sunday
The liturgical seasons
Dec. 1, 2019–Jan. 12: Advent, Christmas
Jan. 13–Feb. 25: Ordinary Time
Feb. 26–May 31: Lent, Triduum, Easter
June 1–Nov. 28: Ordinary Time
Nov. 29–Jan. 10, 2021: Advent, Christmas
Other dates of note
Jan. 24: March for Life
Feb. 3: Iowa presidential caucuses
Feb. 11: New Hampshire presidential primary
March 13: Anniversary of the election of Pope Francis
March 15: N.C.A.A. basketball tournament (“March Madness”) begins
April 22: World Earth Day
June 10: G7 Summit
July 13: Democratic National Convention
July 20: Summer Olympics (Tokyo)
Aug. 24: Republican National Convention
Sept. 29: First presidential debate (at Notre Dame University)
Nov. 3: U.S. Election Day
Anniversaries of historical events
Jan. 17: Prohibition bans the sale of alcohol in the U.S. (1920)
Feb. 11: Nelson Mandela released from prison (1990)
March 24: Assassination of Archbishop Oscar Romero in El Salvador (1980)
March 25: publication of “Evangelium Vitae” (1995)
April 2: death of St. John Paul (2005)
May 8: birth of Fulton Sheen (1895)
May 8: Victory in Europe Day (1945)
May 24: publication of “Laudato Si’” (2015)
Aug. 6: atomic bombing of Hiroshima (1945)
Aug. 18: 19th Amendment gives women the right to vote (1920)
Sept. 26: First televised U.S. presidential debate (Kennedy v. Nixon) (1960)
Sept. 27: Jesuits receive charter from Pope Paul III (1540)
Oct. 24: United Nations founded (1945)
Nov. 11: Mayflower Compact signed (1620)
Nov. 21: “Bloody Sunday”/war of independence in Ireland (1920)
Nov. 23: Nuremberg Trials (1945)
Sources: “Liturgical Calendar for the Dioceses of the United States of America 2020,” U.S. Conference of Catholic Bishops; “2020 Holy Days of Obligation and Solemnities,” relevantradio.com.