Hi there, I’ve just recently started using blender again for the first time in years so I was bound to run into some things I had forgotten.
This is the model I’m working on:
The long object on the back overlaps into the smaller one next to it as demonstrated here:
How do I go about getting rid of the superfluous surfaces and vertices that are within the object?
the second image is useless, as its too closeup. we cant see what it is…
anyway, if its one face overlapping another, then move one of the faces 0.0001cm away 
or just delete one of the faces…
i would actually guess that you are inside the mesh now, since this does not look like anything that could happen form what you got on the first image, if that is the case, then dont bother. its inside the mesh and noone will ever see it 
Select a vertex of the object you want to move then hit L key to select the entire object. Use the G shortcut or the 3D navigator to move the object.
not much of a blender expert by any means, but a possible partial solution, merge the common vertices?
Sorry about that. It was supposed to be an interior shot that shows how the longer shape intrudes in the smaller one.
