When they make LME, they basically brew a batch of beer with just base malt and no hops (unless you get hopped malt extract or use the darker LME's that will have some specialty malts in it). They boil the wort pretty much like you would if you did all grain and then they concentrate it by removing some of the water and sell it. So all you really HAVE to do with it is add water and you have the same post-boil wort they ended up with. You might get a little hot break, but nothing to be really worried about if you do or don't.
You can add it at any point in the boil that your recipe needs it to be added. I do partial mash with large amounts of grain so I pretty much end up with the same wort an all-grain brewer has when I start boiling, just less of it. I treat it like I would an all grain batch through the boil, just smaller.
Then, at the end, I add my LME and boil it just enough to make sure things are sanitary and after cooling I top up with water to my full volume. I'm basically just using a little LME and water to make up the difference between my partial boil and a full boil.
"Science + beer = good!"