When vesting for the liturgy, the cleric
first washes his hands, praying:

Give virtue to my hands, O Lord, that being cleansed from all stain I might serve you with purity of mind and body.

Latin version:
Da, Domine, virtutem manibus meis ad abstergendum omnem maculam ut sine pollutione mentis et corporis valeam tibi servire.

Amice

Then he puts on his:

Amice

Symbolizes: the Helmet of Salvation

The amice is a rectangular piece of white linen with two strings at the upper corners which a cleric uses underneath his alb to cover the neck so that the Roman collar of the cassock is hidden. The word amice comes from the Latin amicire, meaning "to cover" and, because the heads of criminals condemned to death were covered in linen, the amice recalls the humiliation which was put upon Christ.

As he puts on the amice, the priest kisses the Cross on the Amice and prays:

Place upon me, O Lord, the helmet of salvation, that I may overcome the assaults of the devil.

Latin version:
Impone, Domine, capiti meo galeam salutis, ad expugnandos diabolicos incursus.

Alb

Alb

Symbolizes: Purity

The alb is the long white, robe-like vestment worn by all clerics at liturgical celebrations (celebrant, concelebrant, deacon, or acolyte). The alb (from Latin word alba, meaning "white") can be traced to the ancient Roman alb worn under a cloak or tunic; its color symbolizes purity and its form recalls that described in Ezekiel 28:4.

As he puts on his alb, he prays:

Purify me, O Lord, and cleanse my heart; that, being made white in the Blood of the Lamb, I may come to eternal joy.

Latin version:
Dealba me, Domine, et munda cor meum; ut, in sanguine Agni dealbatus, gaudiis perfruare sempiternis.

Cincture

Cincture

Symbolizes: Chastity

The cincture, a symbol of chastity, ties the alb at the waist.

As he ties the cincture, he prays:

Gird me, O Lord, with the girdle of purity, and extinguish in me all evil desires, that the virtue of chastity may abide in me.

Latin version:
Praecinge me, Domine, cingulo puritatis, et exstingue in lumbis meis humorem libidinis; ut maneat in me virtus continentia et castitatis.

Maniple

Maniple

Symbolizes: the acceptance of suffering

The maniple is a narrow strip of linen, of the same color as the chasuble, suspended from the left forearm so that if falls equally on both sides of the arm. It is to remind the cleric that he must patiently bear the cares and sorrows of this earthly life in the service of God and for Heavenly reward.

As he puts on the maniple, he kisses the Cross on the maniple and prays:

Grant, O Lord, that I may so bear the maniple of weeping and sorrow, that I may receive the reward for my labors with rejoicing.

Latin version:
Merear, Domine, portare manipulum fletus et doloris; ut cum exsultatione recipiam mercedem laboris.

In the Tridentine liturgy, the bishop puts on the maniple at the Altar after the Confiteor; other clerics put it on in the sacristy before the service.

Stole

Stole

Symbolizes: the clerical office, immortality, and the Yoke of Christ

The stole, matching the liturgical color, is a long, scarf-like vestment worn over the alb and under the dalmatic/chasuble. The priest wears the stole around his neck so that it hangs equally down his chest in front or forms an X-shaped Cross; the deacon wears his stole over the left shoulder and tied at his right side; the Bishop wears his stole so that it hangs equally down his chest.

As he puts on the stole, the priest kisses the Cross on the stole and prays:

Restore unto me, O Lord, the stole of immortality, which was lost through the guilt of our first parents: and, although I am unworthy to approach Your sacred Mysteries, nevertheless grant unto me eternal joy.

Latin version:
Redde mihi, Domine, stolam immortalitatis, quam perdidi in praevaricatione primi parentis: et, quamvis indignus accedo ad tuum sacrum mysterium, merear tamen gaudium sempiternum.
 

     Chasuble

Chasuble, Dalmatic, or Cope

Priest for the Eucharistic Liturgy: Chasuble
Symbolizes: Charity and the Yoke of Christ

The chasuble, also matching the liturgical color, is is the long, often ornate, sleeveless poncho-like garment worn by priests and bishops over the alb and stole during the sacrifice of the Mass.

As he puts on the chasuble, he prays:

O Lord, Who said: My yoke is easy and My burden light: grant that I may bear it well and follow after You with thanksgiving. Amen.

Latin version:
Domine, qui dixisti: Iugum meam suave est et onus meum leve: fac, ut istud portare sic valeam, quod consequar tuam gratiam. Amen.

Deacon for the Eucharistic Liturgy: Dalmatic
Symbolizes: Charity, Justice, and the sufferings of Christ

Instead of a chasuble like a priest wears, the deacon wears the sleeved dalmatic, also matching the liturgical color, over his alb and stole. Bishops also wear a dalmatic at major solemn feasts and ordinations.

As he puts on the dalmatic, the deacon or bishop prays:

Lord, endow me with the garment of salvation, the vestment of joy, and with the dalmatic of justice ever encompass me.

Priest or Deacon for non-Eucharistic Liturgy: Cope
The cope is a large mantle worn by clerics at some liturgical celebrations (but not at the Mass) -- for example, during Processions and Benedictions of the Blessed Sacrament. It matches the color of the liturgy and is worn in the same way as the chasuble or dalmatic.
 

Biretta

The biretta is a tri-cornered or square-shaped hat with silk trim, tuft (except for the birette of seminarians and cardinals) and raised wings, called "horns," on top. It is made of scarlet silk for cardinals, violet silk for bishops, and black merlino for priests, deacons, and seminarians.

In addition to the above,
the Bishop wears a:

Pectoral Cross

The pectoral cross is a cross, usually about 6 inches in height, worn around the neck of a bishop and suspended by either cord (in liturgical vestments or choir) or chain (in abito piano). The cord is scarlet and gold for a cardinal; green and gold for a bishop. The pectoral cross is worn on the chest of prelates so as to keep the Cross close to their hearts.

Crozier

The crozier is the shepherd's staff used by bishops. The crozier has always been in the Church a symbol of the bishop's pastoral role. In the very early Church, it was made of wood, but in the early Middle Ages metal (silver and gold, depending on rank) was used instead. Wooden croziers again began to be used during the time of Vatican II and are common today.

Popes don't use a crozier, and only since the time of Vatican II have they used a crozier-like staff called the "pastoral staff." The pastoral staff is silver with a crucifix at the top.

Episcopal Ring

When a Bishop is consecrated as Bishop, he receives a ring representing his office (Cardinals receive their own special ring, also). The Pope's ring, known as the "Fisherman's Ring," is the personal and unique seal of that reigning Pontiff and is (or at least used to be) destroyed on his death.

Zucchetto

The zucchetto is the silk yarmulka-like skullcap worn by bishops. The Pope's zucchetto is white; the cardinals' zucchetti are scarlet; the bishops' zucchetti are violet. Priests may use a black cloth zucchetto for everyday wear, but not during the liturgy.

Mitre

The mitre imitates the Old Testament priestly headcovering and is the headdress of bishops, worn at liturgical functions. It is either precious, golden (orphreyed), or simple (simplex). The precious mitre is worn by celebrants, the simple by concelebrants, and the golden by the celebrant at an ordination. All cardinals wear a damasked mitre (simplex) in presence of the Pope. It is very tall and made of layered white damask silk.

In addition to the above,
a Metropolitan (Archbishop) wears a:

Pallium

The pallium is worn only by archbishops (in their own dioceses), patriarchs, and the Pope, as symbol of their authority. It's a band of white wool adorned with 6 small black crosses, worn around the neck with extensions front and back, and pinned to the chasuble in three places about the neck. The non-silk part of the pallium is made of white wool, part of which is supplied by two lambs presented annually by the Lateran Canons Regular on the feast of St. Agnes (21 January). The lambs are solemnly blessed on the high altar of that church after the pontifical Mass, and then offered to the pope, who sends palliums made of their wool to the archbishops.

In addition to the above, the Pope wears a:

Fanon

The fanon is a vestment , rarely used nowadays, reserved for the Pope during a pontifical Mass. It consists of a double mozzetta (short shoulder-cape worn by bishops outside the liturgy), the first going under the stole and the second over the chasuble.