The Catholic Week and Month

Week

Fridays are penitential days and Catholics are to keep in mind Christ's suffering and to sacrifice something for the sake of penance and discipline. Catholics fulfill this duty by abstaining from meat and making other penances.

Saturdays are, traditionally, the days Catholics go to Confession in preparation for receiving the Eucharist on Sundays, but of course you can go to Confession on any day..

Sundays are, of course, the day for renewing Christ's once and for all Sacrifice during the Sacrifice of the Holy Mass. Because Christ rose from His tomb on Sunday, Sabbath was changed from Saturday to Sundays, or "the Lord's Day." On this day we fulfill God's Third Commandment, to "remember the Sabbath day [which means "rest", not "Saturday"], to keep it holy." We refrain from unnecessary servile work and fulfill our "Sunday Obligation" to attend Mass.

Month

Footnotes:
¹ Tuesdays are also the day for honoring the Holy Face and, unofficially, honoring St. Anthony of Padua. On the Tuesday after St. Anthony's death, the day his funeral cortege took his body to the church, many miracles took place, so this day is commemorated in his honor, often by praying a Novena to St. Anthony either for thirteen consecutive Tuesdays or perpetually.

A special Novena to St. Dominic, St. Anne and St. Martha is also made on 9 consecutive Tuesdays or on all Tuesdays by some Catholics.

² On Wednesdays, many Catholics make a special devotion to St. Joseph by going to Mass on the first Wednesdays of 9 consecutive months and offering their Communions in his honor and for the salvation of the dying..

³ On Thursdays, many Catholics make "Holy Hour," that is, they spend an hour in adoration of the Blessed Sacrament as an aspect of devotion to the Sacred Heart.

⁴ On Fridays, many Catholics make what is known as the "First Fridays Devotion" in honor of the Sacred Heart. This entails going to Mass and receiving Communion in reparation to the Sacred Heart on the first Friday of the month for 9 consecutive months.

⁵ On Saturdays, many Catholics make what is called the "First Saturdays Devotion" which entails going to Mass and receiving Communion for the first Saturday of the month for 5 consecutive months in reparation to the Immaculate Heart of Mary.   

Partial Text courtesy of Fisheaters

The Catholic Year Calendar-Related Customs

Below are links to pages that describe customs and devotions related to the liturgical year.
 Dates in italics are movable.