Here’s a good and patristic overview for you from +John of Damascus:
“But if you inquire as to how this takes place, it is enough for you to know that it is effected by the Holy Spirit. The manner of the change can in no way be understood. But one can put it well thus, that just as in nature, bread, by eating, and wine and water, by drinking, are changed into the body and blood of the eater and drinker, yet not becoming a different body from the former one; so the bread of the Table, as also the wine and water, are supernaturally changed by the invocation and presence of the Holy Spirit into the Body and Blood of Christ, and are not two, but one and the same.”
This occurs, by the grace of God alone, at this point during the Divine Liturgy:
“Priest (in a low voice): It is proper and right to sing to You, bless You, praise You, thank You and worship You in all places of Your dominion; for You are God ineffable, beyond comprehension, invisible, beyond understanding, existing forever and always the same; You and Your only begotten Son and Your Holy Spirit. You brought us into being out of nothing, and when we fell, You raised us up again. You did not cease doing everything until You led us to heaven and granted us Your kingdom to come. For all these things we thank You and Your only begotten Son and Your Holy Spirit; for all things that we know and do not know, for blessings seen and unseen that have been bestowed upon us. We also thank You for this liturgy which You are pleased to accept from our hands, even though You are surrounded by thousands of Archangels and tens of thousands of Angels, by the Cherubim and Seraphim, six-winged, many-eyed, soaring with their wings,
Priest: Singing the victory hymn, proclaiming, crying out, and saying:
People: Holy, holy, holy, Lord Sabaoth, heaven and earth are filled with Your glory. Hosanna in the highest. Blessed is He who comes in the name of the Lord. Hosanna to God in the highest.
Priest (in a low voice): Together with these blessed powers, merciful Master, we also proclaim and say: You are holy and most holy, You and Your only-begotten Son and Your Holy Spirit. You are holy and most holy, and sublime is Your glory. You so loved Your world that You gave Your only begotten Son so that whoever believes in Him should not perish, but have eternal life. He came and fulfilled the divine plan for us. On the night when He was betrayed, or rather when He gave Himself up for the life of the world, He took bread in His holy, pure, and blameless hands, gave thanks, blessed, sanctified, broke, and gave it to His holy disciples and apostles saying:
Priest: Take, eat, this is my Body which is broken for you for the forgiveness of sins.
People: Amen.
Priest (in a low voice): Likewise, after supper, He took the cup, saying:
Priest: Drink of it all of you; this is my Blood of the new Covenant which is shed for you and for many for the forgiveness of sins.
People: Amen.
Priest (in a low voice): Remembering, therefore, this command of the Savior, and all that came to pass for our sake, the cross, the tomb, the resurrection on the third day, the ascension into heaven, the enthronement at the right hand of the Father, and the second, glorious coming.
Priest: We offer to You these gifts from Your own gifts in all and for all.
People: We praise You, we bless You, we give thanks to You, and we pray to You, Lord our God.
Priest (in a low voice): Once again we offer to You this spiritual worship without the shedding of blood, and we ask, pray, and entreat You: send down Your Holy Spirit upon us and upon these gifts here presented.
Priest: And make this bread the precious Body of Your Christ.
Amen.
Priest: And that which is in this cup the precious Blood of Your Christ.
Amen.
Priest: Changing them by Your Holy Spirit. Amen. Amen.
Amen.”
+Gregory Palamas wrote in the 14th century: “... by this flesh [of Christ in the Eucharist] our community is raised to heaven; that is where this Bread truly dwells; and we enter into the Holy of Holies by the pure offering of the Body of Christ”
How do we “know” this? It’s a matter of faith, cyc, not knowledge, at least not knowledge of a mundane variety. Christians, the overwhelming majority of Christians including a number of Protestant type Christian groups, have always believed in the Real Presence. Well, I say always, let’s say since the year 100 or so at least (+Ignatius of Antioch). The Church teaches about all sorts of miracles, big and small and personal, which have occurred during the Liturgy and surrounding the Eucharist. They are not really uncommon, cyc. They have actually been experienced by people who are posters on this website. Beyond that, I have no “proof” at all for you.
Faith has a basis unlike credulity.
Damascus makes the statement, “.......supernaturally changed by the invocation and presence of the Holy Spirit into the Body and Blood of Christ, and are not two, but one and the same.”
Upon what basis? The words of Christ? Then the Christ is law breaker and his disciples as well.
By divine inspiration? Does Damascus claim such? Are his words more inspiried than the Gospels?
A simple meal of remembrance, and remembrance was its stated purpose, becomes by retrospective elaboration into a mysterious, throw up the hands—no one can understand this! ritual due to insistance that “is” can only mean one thing despite evidence to the contrary.
I don’t ask for proof but simply consistancy with God’s own word.