Very, very carefully!! As the old carpenter's adage goes, "Measure twice, Cut once." In other words, make certain that you know what you are removing before you cut it off because it is hard to put back.
Areas to be cut out like that are always different. If you only need to remove a small amount of styrene, a file or sanding sticks might work. If there is a lot, a Dremel or razor saw might be better suited to get you close, and then switch to a file and finally sanding sticks or sandpaper.
As mentioned by the others, don't try and cut down to the finished line. Go slowly and carefully when you start getting close and dry fit frequently. Going too far is a bad thing!