My biceps always get sore when I do lat pull-downs — how do I get my back more involved?

Take your arms and hang them comfortbly by your sides. Start with about this width. Outside of that will be wide grip, inside of that will be narrow grip.

Grip the bars at normal width to begin with. Now, here is the key. Instead of pulling all the way down, instead, focus on keeping your arms straight and simply contract your back (mainly your lats and the scapulae, or the muscles between your shoulder blades) - in other words, pull the bar down as far as possible without bending your arms (I don't want your arms locked out, but don't excessively bend them, either). Your range of motion will probably be just a few inches, and that's fine. This is what is called scapular retraction.

Try doing a few of your sets only doing this - only involving the back.

After you are used to that and how it feels, then start to pull the bar all of the way down. However, don't think of bending your arms to get the bar down, although they will bend ... instead, think of pulling from your back, like there is a string that starts in your back and runs through your arms to the bar, and you are pulling that string to bring the bar down.

See how that makes you feel.