In a congregational church, final authority under Christ rests with the gathered membership itself, ordinarily exercised at a members' meeting that calls and can dismiss its own pastor, admits and disciplines its own members, approves its own budget, and holds its own property, often through a locally elected board of deacons or trustees rather than through any outside body. No bishop assigns the minister, no presbytery reviews the congregation's decisions, and no synod can overrule a vote taken by the members themselves.
This does not mean isolation. Congregational churches routinely join voluntary associations, conventions or fellowships, the Baptist conventions being the clearest example, to cooperate on missions, seminaries, publishing and disaster relief, and these bodies can and do withdraw fellowship from a congregation whose belief or conduct they judge to have broken faith with the group. But withdrawing fellowship is the limit of the association's power: it can decline to associate, never command.
The tradeoff is real and openly debated within congregationalist churches themselves. The system protects local independence and rapid, direct accountability to the gathered members, at the cost of the coordinated discipline, shared resources and doctrinal uniformity that a connectional system, whether episcopal or presbyterian, can provide across many congregations at once.