This is the third post on the Church in my ongoing series, theology in bullet points. The first unit in this series had to do with God and Creation (book here), and the second unit was on Christology and Atonement.
We are now in the third and final unit: The Holy Spirit and the Church. The first set of posts in this final unit on the Spirit and the Church was on the Holy Spirit.
The true Church is both visible and invisible.
1. The true, invisible Church is visible in that those who are in Christ inevitably will come together to worship, disciple, fellowship, and participate in God's mission to the world. Even though the true Church is invisible, it is not individual. The Church is a corporate entity.
When Paul tells the Corinthians that "you are God's temple" and that "God's Spirit dwells in you (1 Cor. 3:16), he does not use the singular word for "you" in Greek, but the plural. It is the collective body of Christ that is the Church rather than me in my individual body.  We are God's temple far more than I am God's temple.
So it is questionable whether a person who claims to be in Christ but never meets together with other believers is truly in Christ unless their circumstances truly prevent them from doing so. God has created us in a way that we need each other for spiritual strength. God often chooses to heal us through others, even though he could do it directly.
Are you discouraged? God could encourage you directly, but he more often uses others. Indeed, there are situations where we cannot even sense God's presence as individuals and, rather than push through the clouds directly, God uses our fellow believers to heal our antennae.  In the mystery of his will, God uses people to do so much of his work on this earth.
2. It does not matter whether you are an introvert or an extrovert. Christians assemble together (e.g., Heb. 10:25). Indeed, the word church in Greek, ekklesia, means an "assembly," a gathering of individuals.  The apostle Paul's primary use of the word is in reference to a local gathering of believers rather than the body of Christ everywhere.
So the first meaning of the word church is in reference to a local gathering of believers, probably gathering in a house. A city like Rome and Ephesus would have many such churches. The church at Corinth seems to have been able to gather together in the house of Erastus, suggesting that Corinth may have only had 40 or 50 believers in the city (cf. Rom. 16:23). 
To refer to all the churches everywhere as the "Church" is thus a figurative expression, a metaphor built off the primarily meaning of a church as a local gathering of believers. The invisible, global, timeless Church is the collection of all the "assemblies of God" (cf. 1 Thess. 2:14) that have met in all times and places for the last two thousand years.
3. Before the Protestant Reformation in the 1500s, there was only one church for any one region. If you lived in the West, you were Roman Catholic. If you lived in the East, you were Orthodox. If you lived in Egypt, you were Coptic. So while these groups might question whether the others were truly in the Church, there was no doubt for those who lived in a particular place as to who was in the church there.
So the church in a specific location was quite visible, even if we might now say that its true membership was invisible even then. But there was no question as to what was a church and what wasn't.
However, the Protestant Reformation raised this question with force: How do you know when you are truly in a church? If the Church is invisible and there is more than one visible, human organization that claims to be the Church or at least part of the Church, how do you know which ones are legitimate and which ones are not?
From this question would develop the "three marks of the Church." A true church is anywhere there is 1) the pure preaching of the gospel, 2) the pure administration of the sacraments, and 3) the practice of church discipline.  This model suggests that a true, visible church--rather than a mere Bible study or meeting for fellowship--is one where someone proclaims the word of God, where individuals are baptized and the Lord's Supper eaten, and where there is enough organization and leadership for church discipline to take place.
Yet the Reformers here no doubt were still reading their own assumptions into these definitions. They were elevating the importance of preaching in keeping with the fact that the Reformation centered on Scripture. In much of their thinking they retained a sense of the sacraments that had developed as much in Christian history as in the Bible, only pruning the number down to two. And they assumed an importance to church structure that fit with the need to counterbalance the power of the Roman Catholic Church. None of these drives were bad, but were they essential?
4. What was a "gathering" in the early church? Perhaps more fundamental for its existence than what they did when they gathered is the mere fact that they did gather, regularly. So first, a visible church is a collection of believers that gathers regularly. As Matthew 18:20 suggests, there is a special, authoritative sense of God's presence when even two or three of God's people are together.
What do they do when they gather regularly? There is a collection of activities that they do, and we need not limit them to say that a church is only a church when they are doing a certain core of them.  They worship together (which often includes the sacraments). They often hear a word from the Lord and instruct each other (often if not usually involving Scripture). They fellowship together. They admonish one another (which can include church discipline and leadership). They participate in the mission of God to redeem the world.
Over time, we might say that a true, visible church will end up doing all these things and that, if it does not, it is perhaps imbalanced in some way. But the core ingredient, the core identifier, is that a group of individuals in the invisible Church are meeting together regularly to do these sorts of things. A true, visible church is a collection of individuals who have the Holy Spirit and are in Christ who meet together regularly to worship, disciple, fellowship, admonish, and spread the gospel in the world.
The Church is invisible, but it meets together in visible churches.
Next week: E4. The church is one body even though it has many members.
 There is arguably nuance even to 1 Corinthians 6:19, which is often taken in relation to my individual, physical body as a temple (a verse often used against smoking). The "yous" in this verse are all plural, leading us to think that, primarily, Paul is again thinking of the collective body of Christ at Corinth. What each man does with his individual body with a prostitute corrupts the whole body of Christ at Corinth. See Kenneth Schenck, 1 and 2 Corinthians: A Commentary for Bible Students (Indianapolis: Wesleyan Publishing House, 2006).
 A book that was once meaningful to me in this regard was David Seamand's Healing of Memories (Colorado Springs: Chariot Victor, 1985).
 Although the image of the church as the "called-out ones" is a helpful illustration, it is not technically accurate. This is an example of the etymological fallacy, where you assume that the history of a word--in this case the words that once came together in Greek history to form the word--determine what the word means. So since ek means "out of" and kalein means "to call," the conclusion is reached that ekklesia means "called out of."
But no Greek thought this any more than we think of "understanding" as "standing under" something. These words had been joined together centuries before the New Testament and people just used the word without thinking of its history. The clearest example of this fact is Acts 19:41, when the city clerk sends a mob away. This verse says that he dismissed this ekklesia.
 See especially Wayne A. Meeks, The First Urban Christians: The Social World of the Apostle Paul (New Haven: Yale University, 2003 ).
 The number varied a little at first. John Calvin, for example, only mentions the first two in his 1536 Institutes of the Christian Religion, but he mentions church discipline elsewhere as a practice of the Church.
 This is a key insight from the philosopher Ludwig Wittgenstein. There is not always a core set of universal characteristics to something we name. Sometimes an "entity" is defined by a looser collection of characteristics and "family resemblances." In other words, there are trends of characteristics for the group that may be prevalent but not universal (e.g., a family may be known for having big noses without everyone in the family having a big nose).