I did this repair successfully, and linked to an album of photos below. I actually took these photos while putting it back together, but I reversed the order to help with taking it apart.

http://imgur.com/a/sRfRM

There's a couple things to watch out for.

First - there's two versions of the screen for the LG Optimus F3. You either have the (LS720/MS659/VM720) screen, which has rounded corners at the top (like mine), or the (MS659/P659), which has square corners at the top. I bought the wrong one, and cracked it trying to grind the corners off at the top.

You will need to use a heat gun to get the old screen off, and I just used an epoxy to attach the new one.

When reassembling, make sure all of your wires are plugged back in. I missed one, and I was getting no signal. Last thing - make sure you put the main center button in before you snap the front screen assembly to the main phone body.