I have Three.Shape which I can apply Extrusion To get a plane I drew a square first and then apply extrusion
var squareShape = new THREE.Shape();
squareShape.moveTo( 0,0 );
squareShape.lineTo( 0, sqLength );
squareShape.lineTo( sqLength, sqLength );
squareShape.lineTo( sqLength, 0 );
squareShape.lineTo( 0, 0 );
var geometry = new THREE.ExtrudeGeometry( squareShape,extrudeSettings);
now a 3D square is appearing on my browser.
Next I want to apply a image texture of 256x256 on its top face. How to do this?
If you look at src/extras/geometries/ExtrudeGeometry.js in THREE.js you will see these comments.
So for example you can say (obviously won't run directly because it is incomplete)
And when you create your mesh you create 2 materials and assign them to your mesh.
Hope this gets you on the right path.
On a side note, related to the other answer, you make want to use extrude to create something that dimensionally is similar to a square but has bevels. One example would be if you were trying to draw dice and wanted to round the edges.
If all you want is a cube why are you extruding? Why don't you use the CubeGeometry.