If you ask that question at a school, you'll be told that the principal is in charge.
If you ask that question at a restaurant, you'll be told that the manager is in charge.
If you ask that question at a tournament, you'll be told that the director is in charge.
If you ask that question at a church, you'll be told that...well, the answers tend to vary.
Of course, most churches will answer that question by saying that God (or at least Jesus) is in charge. For instance, I read on one church's statement of beliefs that, "Christ is the recognized leader of our church, not any person, group, or religious organization." That's fine as far as it goes, but when that answer is put into practice things aren't nearly so simple.
Church polity is the descriptive heading over all the ways that churches and denominations choose to organize and govern themselves. Honestly, I don't know too many people today who care about church polity, and I know even fewer who even know the polity of the church they attend (much less what the phrase means). But just so you know, church polity matters because it answers important and practical questions like:
Who are church leaders accountable to?
How do church leaders and church members relate to one another?
How do people become members of the church?
How are moral/ethical standards upheld?
How are disciplinary actions handled?
These questions and the overall relevance of this topic led Steven Cowan to say, "[T]he issue of church government may not be a doctrine crucial to the esse (being) of the church, but it is a doctrine crucial to the bene esse (well-being) of the church...".
In order to help those unfamiliar with this topic, here is a brief synopsis of the three primary forms of church polity:
1) Episcopal (hierarchical)
These churches/denominations have an episcopate (office of bishop) that is distinct from, and presiding over, the leaders of local churches. The territory overseen by a bishop is called a diocese. Sometimes an archbishop will maintain authority over several other bishops.
Denominations that practice this type of polity include: Roman Catholic, Eastern Orthodox, Anglican, Episcopalian, African Methodist Episcopal, and United Methodist.
2) Presbyterian (representative)
In these churches/denominations the local church (formally called a "session") is ruled by a plurality of elders. These elders are oftentimes selected by the church membership. The session is accountable to the presbytery, which is made up of representatives from several sessions in a specific district or territory. Beyond that, presbyteries are sometimes grouped into synods at the regional level. The highest authority is reserved for the General Assembly (sometimes called the General Synod), which is attended by selected members of the presbytery and oversees the entire denomination.
Denominations that practice this type of polity include: Presbyterian Church USA, Presbyterian Church of America, and Assembly of God.
3) Congregational (democratic)
These churches/denominations have no governing authority that exists outside or above the local church. The lack of centralized authority or hierarchy yields a broad diversity from church to church that is challenging to characterize. Some such churches enter voluntary associations with other similar congregations, while others join conventions for doctrinal guidance and shared finances. Most prominent among churches with this kind of polity are those led by a single elder and those led by a plurality of elders. In the single-elder model, the church chooses a leader (usually called a "Senior Pastor") who is to be assisted by (and sometimes accountable to) a group of deacons who have been elected from within the congregation. In the plural-elder model, there are multiple leaders who are equal in authority and work as a team to teach and lead the church with the ancillary support of the deacons. This situation is similar to the Knights of the Round Table wherein not everyone has a seat at the table, but the ones who do have equal say at the table.
Denominations that practice this type of polity include: Baptist, Church of Christ, Bible Church, Independent, and Non-Denominational.
As for me, my church is Congregational, but I'm not willing to insist on any one of these in particular as "the biblical model." I believe that each one of these can be practiced well and each one can be practiced poorly. In the final analysis, I do think Jim Belcher is wise when he says, "Yes, we want to be organic and missional, and we want the priesthood of believers to be a reality. But at the same time we realize that no local church can survive long and stay true to its calling without explicitly recognized leaders, and I would say, officers. The long history of the church bears this out" .
 Steven B. Cowan, "Introduction" in Who Runs the Church?: Four Views on Church Government, ed. Steven B. Cowan (Grand Rapids: Zondervan, 2004), 11. See also Perspectives on Church Government: Five Views of Church Polity, ed. Chad Owen Brand and R. Stanton Norman (Nashville: Broadman & Holman, 2004).
 Jim Belcher, Deep Church: A Third Way Beyond Emerging and Traditional (Downers Grove: InterVarsity, 2009), 175.
Denominations & Unity
The Work of the Church