Taken from "How to draw a line" - ThreeJS wiki
Assuming you have your scene, renderer and camera set up, you can do this.
var material = new THREE.LineBasicMaterial({
color: 0x0000ff
});
var geometry = new THREE.Geometry();
geometry.vertices.push(new THREE.Vector3(-10, 0, 0));
// Everything from this point, would represent a line
geometry.vertices.push(new THREE.Vector3(0, 10, 0));
geometry.vertices.push(new THREE.Vector3(10, 0, 0));
var line = new THREE.Line(geometry, material); scene.add(line);
// on update
renderer.render(scene, camera);