It is a pious Catholic practice (a longstanding one, at least in the case of the First Fridays) to set aside, each month, the first occurrences of certain days of the week in honor of some particular devotion. These devotions originate in private revelation — that is, in specific visions or other revelations to particular individuals. Such private revelations are not intrinsic to the Catholic faith, but rather are ancillary to it.

Each devotion entails a certain list of requested prayers or acts to be carried out on the first associated weekday of the month. Usually this is done for a certain number of consecutive months. Each devotion has various divine promises associated with it. Because these devotions all involve the worthy reception of Holy Communion, one must be Catholic in order to receive the various promises attached to these devotions. (Holy Communion does not need to be in the context of Mass, meaning the sick and homebound can participate in these devotions as well.)

As you can see from this summary table, three of these devotions (Wednesday, Thursday, and Saturday) originated from private revelations in the 20th century. The First Friday devotion is much earlier, given to Saint Margaret Mary Alacoque in the 17th century.

DevotionIn Honor OfGiven
First WednesdaysThe Pure Heart of Joseph1958
First ThursdaysThe Wounds of Our Eucharistic Lord1949
First FridaysThe Sacred Heart of Jesus1688
First SaturdaysThe Immaculate Heart of Mary1925

I have compiled here a summary of these devotions for your convenience.

First Wednesdays

In Honor Of
The Pure Heart of Joseph
Origin
Given by St. Joseph to Sister Mildred Mary Neuzil on March 30, 1958 in the United States, in a vision as part of the apparitions of Our Lady of America. (Although the Church is still in the process of investigating the supernatural character of the apparitions themselves, the devotional elements associated with the apparition have been endorsed by several bishops.)
Duration
Unlike the other devotions listed here, no particular number of First Wednesdays is specified. Presumably this is intended to be a habitual lifelong devotion. This is easily doable for those who are already in the habit of praying a daily Rosary and going to daily Mass.
Requests
On every first Wednesday:
  1. Recite the Joyful Mysteries of the Rosary in honor of Joseph’s role in the hidden life of the Holy Family, focusing on Joseph’s love for Jesus and Mary and the sorrows Joseph shared with them.
  2. Receive Holy Communion in a state of grace (either during or outside of Mass), in union with Joseph’s love for the Christ Child.
Promises
Joseph says, “Those who honor me in this way will be consoled by my presence at their death, and I myself will conduct them safely into the presence of Jesus and Mary.”

First Thursdays

In Honor Of
The Wounds of Our Eucharistic Lord
Origin
Given by Jesus to Blessed Alexandrina of Balazar (a Portuguese mystic) through private revelation on February 25, 1949.
Duration
Six consecutive months. The number six represents Jesus’s five wounds of the Crucifixion (hands, feet, and side) plus his shoulder wound from carrying the Cross.
Requests
On the First Thursday of each of the six months:
  1. Receive Holy Communion in a state of grace (either during or outside of Mass), “with sincere humility, fervor and love.”
  2. Spend one hour praying in the presence of the Blessed Sacrament, meditating on the wounds of Jesus (particularly his often-overlooked shoulder wound which he received from carrying the Cross) and the sorrows of Mary.
Promises
  1. The granting of all petitions (for both spiritual and corporeal graces) which are made during that hour of prayerful meditation with recourse to the merits of those wounds and sorrows (unless the granting of those requests would cause spiritual harm in some way).
  2. The grace of entering heaven through the advocacy of the Blessed Mother, whom Jesus will bring with him to defend the soul when he meets the soul at the moment of death.

First Fridays

In Honor Of
The Sacred Heart of Jesus
Origin
Given by Jesus to Saint Margaret Mary Alacoque through private revelation sometime before or during the month of May 1688.
Duration
Nine consecutive months. (Nine is the number associated with a novena.)
Requests
On the First Friday of each of the nine months, receive Holy Communion in a state of grace (either during or outside of Mass), in honor of the Sacred Heart of Jesus.
Promises
  1. The grace of final repentance.
  2. Dying in a state of grace.
  3. Dying with the sacraments.
  4. Having the Sacred Heart as secure refuge at the hour of death.

First Saturdays

In Honor Of
The Immaculate Heart of Mary
Origin
Given by Mary to Sister Lúcia (one of the three visionaries of Fátima) in a vision on December 10, 1925 (eight years after the original Fátima apparitions). During additional mystical experiences over the next five years, Sister Lúcia asked Jesus for more flexibility in the timing of the reception of Confession and Communion. Jesus granted these provisions and they are discussed below.
Duration
Five consecutive months.

In 1930 (five years after the revelation of the devotion), Sister Lucia asked Our Lord about the significance of the number five. He replied that this devotion is in reparation for five categories of offenses against the Immaculate Heart of Mary:
  1. Blasphemies against (that is, denial or ridicule of) the Immaculate Conception
  2. Blasphemies against Mary’s perpetual virginity
  3. Blasphemies against Mary’s motherhood (Mother of God and Mother of All Nations)
  4. The crimes of those who plant indifference or contempt towards Mary in the hearts of children
  5. Direct offenses against her sacred images.
Requests
On the First Saturday of each of the five months, do the following, all of which must be done with the explicit interior intention of making reparation to the Immaculate Heart of Mary:
  1. Receive the Sacrament of Penance. (Jesus later told Sister Lúcia that, if it is impossible or unnecessary to go to Confession on the day itself, the individual may satisfy this request by going within 8 days before or even after the First Saturday. If someone went to Confession within the 8 days but didn’t do so with the explicit interior resolution of reparation to the Immaculate Heart, that person may make this intention of reparation during Confession received at the next available opportunity.)
  2. Receive Holy Communion in a state of grace, either during or outside of Mass. (If one is receiving Communion during Mass, the type of Mass does not matter: that is, a Saturday-evening anticipatory Sunday Mass is just as efficacious in satisfying this request as a Saturday-morning Mass. All that matters is that it’s on the Saturday, because Mary’s request is in reference to reception of Communion, not attendance at any specific liturgy. Canonically, a Saturday evening Mass is still on Saturday, even though it fulfills the Sunday obligation. Jesus later told Sister Lúcia that, if one has good reason for being unable to receive Holy Communion on the First Saturday itself, the individual may ask any priest for permission to transfer the fulfillment of this condition to the next day, which would be a Sunday.)
  3. Pray five decades of the Rosary.
  4. Spend an additional 15 minutes silently meditating on any one or more of the mysteries of the Rosary.
Promises
Mary’s assistance at the hour of death with the grace necessary for one’s salvation.