Make line art look like a sketch in Photoshop?

You could get an outline using the Sketch > Photocopy filter

I have removed the background to show what is left. 

If you want to do that use Layer Style > Blend If and drag the highlight end slider to the left.

To knock it out completely, make the layer a Smart Object, and immediately Rasterize it.

This is what it looked like with the white background

What someone like an illustrator/cartoon artis etc would do, is to hand ink in the lines manually.  I personally am a bit shite at that and I have an Intuos 5, and an Xencelabs Pen Display (like a Wacom Cintiq).  It is much easier on the Pen Display, but I still find it difficult to follow the lines.

So what a lot of people do, and that includes industry greats like Bert Monroy, is to stroke workpaths.  You can get perfect placement that way, and stroke the path with whatever preset works best for you.