Like myself, most non-Catholic Christians don't know much beyond Catholics praying "hail Mary full of grace" while holding a rosary. But then again I find that I'm contradicting myself because I've watched Catholic services and I've heard how the priests pray. And actually when watching entire services I don't recall anything that seemed wrong or alien about it. I've attended mass a few times in the past as well. And while I don't recall it clearly, I know I didn't walk out of it thinking "that was weird". The only thing that threw me off some during one mass is that it was very liturgical, so it was simply a matter of fumbling my way through it.
Yes indeed, Catholic Church masses are liturgical, and a high mass, one that includes all the parts and is held on a Sunday or other important feast day, is particularly liturgical; many a stranger would be a little surprised by the standing and sitting and kneeling as well as the sign of the cross and the sung parts in the liturgy, but none of it is like to be so surprising as to offend.
The prayers said by the priest are, in essence, the sort of prayer an Anglican priest might say in their liturgy, and the Eucharistic Prayer, which is the most important from a liturgical perspective, is essentially a recital of the gospel message of salvation in Jesus Christ. Here's an example, from today's mass.
THE EUCHARISTIC PRAYER
Extending his hands, the Priest says:
The Lord be with you.
The people reply:
And with your spirit.
The Priest, raising his hands, continues:
Lift up your hearts.
The people:
We lift them up to the Lord.
The Priest, with hands extended, adds:
Let us give thanks to the Lord our God.
The people:
It is right and just.
The Priest continues with the Preface.
Preface
The renewal of all things in Christ
It is truly right and just, our duty and our salvation,
always and everywhere to give you thanks,
Lord, holy Father, almighty and eternal God,
through Christ our Lord.
In him you have been pleased to renew all things,
giving us all a share in his fullness.
For though he was in the form of God, he emptied himself
and by the blood of his Cross brought peace to all creation.
Therefore he has been exalted above all things,
and to all who obey him,
has become the source of eternal salvation.
And so, with Angels and Archangels,
with Thrones and Dominions,
and with all the hosts and Powers of heaven,
we sing the hymn of your glory,
as without end we acclaim:
The Priest concludes the Preface with the people singing or saying aloud:
Holy, Holy, Holy Lord God of hosts.
Heaven and earth are full of your glory.
Hosanna in the highest.
Blessed is he who comes in the name of the Lord.
Hosanna in the highest.
After this the congregation kneels for the remainder of the Eucharistic Prayer.
Eucharistic Prayer I: "The Roman Canon"
The Priest alone recites:
To you, therefore, most merciful Father,
we make humble prayer and petition
through Jesus Christ, your Son, our Lord:
that you accept
and bless ✠ these gifts, these offerings,
these holy and unblemished sacrifices,
which we offer you firstly
for your holy catholic Church.
Be pleased to grant her peace,
to guard, unite and govern her
throughout the whole world,
together with your servant N. our Pope
and N. our Bishop,
and all those who, holding to the truth,
hand on the catholic and apostolic faith.
Remember, Lord, your servants (N. and N.)
and all gathered here,
whose faith and devotion are known to you.
For them, we offer you this sacrifice of praise
or they offer it for themselves
and all who are dear to them:
for the redemption of their souls,
in hope of health and well-being,
and paying their homage to you,
the eternal God, living and true.
In communion with those whose memory we venerate,
especially the glorious ever-Virgin Mary,
Mother of our God and Lord, Jesus Christ,
and blessed Joseph, her Spouse,
your blessed Apostles and Martyrs,
Peter and Paul, Andrew,
(James, John,
Thomas, James, Philip,
Bartholomew, Matthew,
Simon and Jude;
Linus, Cletus, Clement, Sixtus,
Cornelius, Cyprian,
Lawrence, Chrysogonus,
John and Paul,
Cosmas and Damian)
and all your Saints;
we ask that through their merits and prayers,
in all things we may be defended
by your protecting help.
(Through Christ our Lord. Amen.)
Therefore, Lord, we pray:
graciously accept this oblation of our service,
that of your whole family;
order our days in your peace,
and command that we be delivered from eternal damnation
and counted among the flock of those you have chosen.
(Through Christ our Lord. Amen.)
Be pleased, O God, we pray,
to bless, acknowledge,
and approve this offering in every respect;
make it spiritual and acceptable,
so that it may become for us
the Body and Blood of your most beloved Son,
our Lord Jesus Christ.
On the day before he was to suffer,
he took bread in his holy and venerable hands,
and with eyes raised to heaven
to you, O God, his almighty Father,
giving you thanks, he said the blessing,
broke the bread
and gave it to his disciples, saying:
TAKE THIS, ALL OF YOU, AND EAT OF IT,
FOR THIS IS MY BODY,
WHICH WILL BE GIVEN UP FOR YOU.
In a similar way, when supper was ended,
he took this precious chalice
in his holy and venerable hands,
and once more giving you thanks, he said the blessing
and gave the chalice to his disciples, saying:
TAKE THIS, ALL OF YOU, AND DRINK FROM IT,
FOR THIS IS THE CHALICE OF MY BLOOD,
THE BLOOD OF THE NEW AND ETERNAL COVENANT,
WHICH WILL BE POURED OUT FOR YOU AND FOR MANY
FOR THE FORGIVENESS OF SINS.
DO THIS IN MEMORY OF ME.
After the words of Consecration the priest says:
The mystery of faith.
The people continue, acclaiming:
Either:
We proclaim your Death, O Lord,
and profess your Resurrection
until you come again.
Or:
When we eat this Bread and drink this Cup,
we proclaim your Death, O Lord,
until you come again.
Or:
Save us, Saviour of the world,
for by your Cross and Resurrection
you have set us free.
Therefore, O Lord,
as we celebrate the memorial of the blessed Passion,
the Resurrection from the dead,
and the glorious Ascension into heaven
of Christ, your Son, our Lord,
we, your servants and your holy people,
offer to your glorious majesty
from the gifts that you have given us,
this pure victim,
this holy victim,
this spotless victim,
the holy Bread of eternal life
and the Chalice of everlasting salvation.
Be pleased to look upon these offerings
with a serene and kindly countenance,
and to accept them,
as once you were pleased to accept
the gifts of your servant Abel the just,
the sacrifice of Abraham, our father in faith,
and the offering of your high priest Melchizedek,
a holy sacrifice, a spotless victim.
In humble prayer we ask you, almighty God:
command that these gifts be borne
by the hands of your holy Angel
to your altar on high
in the sight of your divine majesty,
so that all of us, who through this participation at the altar
receive the most holy Body and Blood of your Son,
may be filled with every grace and heavenly blessing.
(Through Christ our Lord. Amen.)
Commemoration of the Dead
Remember also, Lord, your servants N. and N.,
who have gone before us with the sign of faith
and rest in the sleep of peace.
Grant them, O Lord, we pray,
and all who sleep in Christ,
a place of refreshment, light and peace.
(Through Christ our Lord. Amen.)
To us, also, your servants, who, though sinners,
hope in your abundant mercies,
graciously grant some share
and fellowship with your holy Apostles and Martyrs:
with John the Baptist, Stephen,
Matthias, Barnabas,
(Ignatius, Alexander,
Marcellinus, Peter,
Felicity, Perpetua,
Agatha, Lucy,
Agnes, Cecilia, Anastasia)
and all your Saints;
admit us, we beseech you,
into their company,
not weighing our merits,
but granting us your pardon,
through Christ our Lord.
Through whom
you continue to make all these good things, O Lord;
you sanctify them, fill them with life,
bless them, and bestow them upon us.
At the conclusion of the Eucharistic Prayer the Priest takes the chalice and the paten with the host and, raising both, he alone says:
Through him, and with him, and in him,
O God, almighty Father,
in the unity of the Holy Spirit,
all glory and honour is yours,
for ever and ever.
Amen.