don't erase, use the pen tool. make sure the paths option is turned on (same place you would change brush size with the brush tool), it's one of several buttons. use the pen tool and click along the outside edge one by one. each click adds a point linked to the last one.
if you make a mistake, use ctrl+alt+z to back up. click all the way round (straight edges are easy, they only need a few points along the edge, but curves will require a lot more to get a nice smooth curve. it helps to zoom in to 300 or 400% while doing this btw) until you get back to the start. click on the first point you laid and it will complete the path.
now right click inside the path, and select make selection. in the box that pops up, make sure anti-aliase is turned on and feather is set to 0.
that will select your object, now just ctrl+c, and then ctrl+v to paste onto your background which you have lined up in another window. hope that helps!
before you try cutting planes out, try something simple first, get the hang of it. if you are still really stck you can try to use the magic wand. try setting the tolerence setting to 15 and select the thing as cleanly as possible (make sure the anti-aliase setting is turned on in the tool options as well) once done just ctrl+c and paste. this method isn't as clean or sharp though, and it often doesn't look nearly as good. it is great for cutting small objects out though, like planes in the distance
