Jonathon, thanks for asking for a basic definition of a “Christian.” It’s much easier to call ourselves and others than to actual identify what we mean.
One of the major difficulties in defining what a Christian is (and, by implication, isn’t–which is important) is at the intersection of (1) our concern for both orthodoxy and orthopraxy and (2) the holy love of God manifest in his grace in the person of Jesus Christ. Said a little differently, perhaps we would say that we’re concerned not to get into “works-righteousness,” but we also recognize that being a Christian ought to entail a change in how we behave. A second major difficulty involves how we connect eternal salvation with being a Christian–this makes the conversation awfully personal awfully quick.
That said, I’ll suggest that a Christian is a person whose life is being drawn God-ward within the community of God’s people through the grace of God in Jesus Christ, the power of God in the Holy Spirit, and by personal participation in God’s work within oneself.