This is a layman's terms insight into the making of the shots below.
These last two examples are taken from one of the angles that is amongst the most difficult of the whole shoot to pull off.
The first part comes with the filming itself. The shot must be filmed identically twice. Same lighting, same angle, everything. If someone bumps the camera, you start over. If a light gets dimmed or bumped in the slightest, it's game over. It's tedious and meticulous.
The scene is filmed once with Danny up front as such:


Then again with him in back on the drums, similar to the still below:


You also have to be careful not to let anything be disrupted on set during the downtime of the costume change.
Once you get around to post production time, you load the first clip with Danny at the forefront into a program called Shake (the program of choice for many Academy Award winning effects artists).
From there you have to trace a series of dots around Danny in any areas where an underlying image will need to be seen, as illustrated by the yellow dotted lines below.

Then you must shift each of these dots, tracking his movement frame by frame.
A clip such as this one take has approximately 6500 individual frames, almost all of which need individual minor alterations one by one.
Once you're all done (likely several days later), you composite your cookie cutter shot over the top of the alternate take with Danny in the back on the drums. It's also advisable to apply a slight feather effect to the edges to hide the seams where the two images are overlaid.
At this point, you will end up with a full take that should look like the two clips immediately below.
From there you have to identify any blemishes in the image of the final take. There will be dozens, more than likely.
You can either go back into Shake and tweak things until its all perfect, which I find to be a time consuming pain in the ass, or you can look over it paint out the flaws frame by frame in Photoshop.
While that may sound really tedious, I've actually found it to go considerably quicker and easier than the preceding option. May times the particular flaws with only last for a mere couple of frames and can be cleaned up within minutes.
When you're all done, you have a polished image ready for prime time.
And to think, I think the above description actually makes it sound easier than it actually is...