How do we encounter Christ at the Lord's Supper?
Those who rightly, worthily, and in faith eat the broken bread and drink the blessed cup partake of the body and blood of Christ in a spiritual manner until he comes.
Catechism for the Global Methodist Church, question 44
28And they drew near to the village where they were going, and he acted as though he were going farther. 29And they urged him, saying, "Stay with us, because it is toward evening and the day is already far spent." And he went in to stay with them. 30And it happened that when he reclined at table with them, he took the bread, blessed it, and after breaking it gave it to them. 31Then their eyes were opened, and they recognized him; and he vanished from them. 32And they said to one another, "Were not our hearts burning within us while he was speaking to us on the road, while he was opening the Scriptures to us?"
53Therefore Jesus said to them, "Truly, truly, I say to you, unless you eat the flesh of the Son of Man and drink his blood, you have no life in yourselves." 54The one eating my flesh and drinking my blood has eternal life, and I will raise him up on the last day. 55For my flesh is true food, and my blood is true drink. 56The one eating my flesh and drinking my blood remains in me, and I in him. 57Just as the living father sent me and I live through the father, so the one eating me will also live through me. 58This is the bread that came down out from heaven, not just as the fathers ate and died; the one eating this bread will live toward the age.
23For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread. 24And when he had given thanks, he broke it and said, "This is my body which is for you; do this in remembrance of me." 25In the same way also the cup, after supper, saying, "This cup is the new covenant in my blood; do this, as often as you drink it, in remembrance of me." 26For as often as you eat this bread and drink the cup, you proclaim the death of the Lord until he comes. 27Therefore whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of the body and blood of the Lord. 28Let a person examine himself, and so eat of the bread and drink of the cup. 29For anyone who eats and drinks without discerning the body eats and drinks judgment on himself.

This question answers the oldest dispute about the Supper: in what way is Christ present, and who receives him. The answer is the last sentence of Article VI of the Confession of Faith: "Those who rightly, worthily and in faith eat the broken bread and drink the blessed cup partake of the body and blood of Christ in a spiritual manner until he comes." Article XVIII of the Articles of Religion fills this out. It rejects transubstantiation, teaches that "the body of Christ is given, taken, and eaten in the Supper, only after a heavenly and spiritual manner," and says that "the means whereby the body of Christ is received and eaten in the Supper is faith."
The phrase partake of the body and blood of Christ is a real claim, and the church's standards do not soften it. Jesus says that "unless you eat the flesh of the Son of Man and drink his blood, you have no life in yourselves" (John 6:53) and that "the one eating my flesh and drinking my blood remains in me, and I in him" (John 6:56). He ends the discourse with the promise, (John 6:58). In a spiritual manner tells how this happens: by the Holy Spirit, received through faith, with the bread and wine remaining bread and wine. The Emmaus story is the catechism's picture of this encounter. Jesus "took the bread, blessed it, and after breaking it gave it to them. Then their eyes were opened, and they recognized him" (Luke 24:30-31).
Rightly, worthily, and in faith comes from Paul's warning to Corinth. He says that "whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of the body and blood of the Lord," and so "let a person examine himself, and so eat of the bread and drink of the cup" (1 Corinthians 11:27-28). The failure Paul had in view was eating "without discerning the body" (1 Corinthians 11:29). Until he comes is Paul's phrase too: "as often as you eat this bread and drink the cup, you proclaim the death of the Lord until he comes" (1 Corinthians 11:26).
John Wesley taught that self-examination is required and that a sense of one's own unworthiness is no reason to stay away, since the Supper is given for sinners who repent and trust Christ. A Methodist comes to the table after self-examination and in faith, expecting to meet the risen Lord as the two at Emmaus did.