I was given a pair of older shimano shifters that were taken off a 1975/6 volkscycles bike. They seem like they were put together incorrectly however these are my first pair. Here are some pictures to help.

What am I missing? Why do you think they're put together wrong? Is there something about them that doesn't work?

It seems like the levers are either on the wrong side or positioned incorrectly. It could be completely fine for all I know.

I agree with FBinNY and, based on your pictures, see nothing wrong with those shifters. Since they aren't indexed, there is very little that can be assembled incorrectly.

How do you identify the left and the right lever?

Non-index levers doen't have to be left or right since they don't have clicks to deal with. The one you put on the right side of the bar is right, the one left over is the left.

That's assuming they are indexed. If both are in friction, it doesn't really matter which is which. I'm pretty sure a few manufactures (Suntour, I'm looking at you) just used the exact same shifter for both sides.

I think you misread my post, we've established that they are non-indexed. That means that whichever one you put on the right side is right (unless you look in the mirror) and the other is left.

Shimano had some counter balance spring bar end levers, those may be it.
they matched the return spring in the derailleur itself.

Same era Sun tour used the power ratchet mech

Ideal setup I found was 1 of each .. ratchet rear , counterbalance spring front.

About the only thing I can think of to prefer one side or the other is to install both shifters so their tension adjustment bolt is to the outside. It's easier to get a wrench or screwdriver on them that way. Functionally, they are interchangable.

That is good to know! It was irritating me for awhile. Thanks for the great info!