Part of the reason I'm writing some of this stuff is as a "way-marker" - so that when I come out of theological college, I (and others) have got a reference to know where I was at when I went in.
An increasing number of evangelicals these days seem to be adopting what I believe is called the Zwinglian model of Communion - that when we share the bread and the wine, it is only a reminder of what Jesus did for us. Some of them would then go on to say that it therefore is only something secondary in the life of the Church. Of course, I disagree with both of those.
Communion - What is Going On?
I think the passage which most easily stops the Zwinglian view of communion is this one:
The cup of blessing that we bless, is it not a participation in the blood of Christ? The bread that we break, is it not a participation in the body of Christ? Because there is one bread, we who are many are one body, for we all partake of the one bread. Consider the people of Israel: are not those who eat the sacrifices participants in the altar?
1 Corinthians 10:16-18, ESV
I've never come across a satisfactory Zwinglian treatment of that. When we share communion, it is a participation in the body and blood of Christ.
That fits perfectly the sacrificial symbolism in Jesus' death as well. He is the perfect sacrifice for our sins. And how did the Israelites participate in the sacrifice? By eating the body of the sacrifice. How do we participate in Jesus' sacrifice for us? By eating his body and drinking his blood.
Drinking the blood of sacrifices was of course forbidden in the Old Testament - blood was used for external sprinkling to purify things. But we drink it - it is a better participation in the sacrifice than was possible under the Old Covenant, and it is internal in its effects, not just external.
That isn't to say, of course, that Jesus is re-sacrificed at Communion. That's a horrible idea and totally against what the Bible says. Jesus died once for all, on the cross, at Calvary, 2000-odd years ago. Sharing the bread and wine now is a timebound participation in Jesus' eternal, once-for-all, sacrifice.
What about the bread and wine?
The Roman idea of transsubstantiaton seems to be based on an Aristotelian idea that there is a distinction between the "accident" of something (what it looks like, what it's made of) and the "substance" of something (what it really is). They'd then say that the "accident" of the bread and wine stays the same, but that the "substance" changes into body and blood. I think that's bunk, for the simple reason that it seems to have abosorbed far too much bad philosophy.
I think what Jesus meant when he said "This is my body" was quite clear - that by eating it, the effect was as if they had eaten Jesus' body and participated in the sacrifice. So there is a Real Presence, but it is not a Real Physical Presence. The bread and the wine, while it should be treated with reverence, is not Jesus. It is bread and wine. But it is a means by which we receive Jesus.
Who can preside?
I'm happy to abide by Church discipline on this one, but as far as I can tell, God is the one who acts at Communion. It should be a Christian presiding, and they should be a recognised leader within the Church. Does it matter if they've been ordained or not? Not to me.