I've been trying to describe this effect on google and got no useful results. Seems like its a mix between a tint via the overlay and the offset?
Here is another example, but the effect seems less pronounced.
The effect is "bad black level". I don't know why anyone would want to deliberately do this, but we can deconstruct how it was done in this case.
Here is the original:
The darkest areas are (.049, .033, .329), which is bluish as we'd expect just from looking at this picture.
Here is the darkest area set to full black (the bluish bias subtracted off):
Now there seems to be a yellow cast. That makes sense if we assume the blue range was squished to make room for the low-end bias. Simply stretching the blue to cover the bias that was removed yields:
That's a bit better. To really fix the color we need a good white (or any known shade of gray really) reference, which we don't have in this picture. The text was artificially added, so doesn't tell us anything about the original colors of the photographed scene. We can try using the reflections off the whites of the eyes, but reflections are usually very unreliable color references. Here is using the refection off the right eye:
The color is better, and not worth trying to tweak further because it's pretty clear now what was done to this picture. Basically, the blue channel was squished to 2/3 its range, and a 1/3 offset added at the low end. In other words original black maps to (0, 0, .33) and original white to (1, 1, 1) as usual.
Seems to me that in order to get this effect,
as jp89 mentioned, it's all about tweaking the colours and contrasts.
You'll want to look at increasing an RGB value, add a new layer on top with a solid colour and change the opacity, then you'll need to look at changing the curve values to increase/decrease highlights and shadows etc.
I've just had a quick google and I think the effect you're looking for is called 'Dreamy'.
If you google terms such as "Dream", "Retro", "Vintage" and so on... you'll get quite a few results covering the type of picture you've shown above.
However if you don't want to use Photoshop, you can use software such as DxO Filmpack. Obviously, there are many other software application that can offer the same features. I only mentioned that one because I use it from time to time.