The basic setup goes like this:
In Edit Mode Unwrap the faces where you want the image to be, so you can use UV coordinates to precisely map the image texture.
To do that select the faces and press U (depending on the shape you might need different a projection, in this I used "sphere projection" but for your mesh it might be different)
Open the Node Editor window in shader and object mode.
On a MixRGB node use the Alpha channel of the image as the Factor to control how the image colors are overlaid on top of the color of the shader (so that only the transparent parts of the PNG file become the color of the shader, the rest will be the color of the overlaid image) Pay special attention to the order in which the sockets are connected.
As an alternative, you can use the image's transparency as a factor on Mix Shader node. That will to control how a shader that uses the colors of your image texture combines with another shader.
And, just for fun, you can use the alpha information as bump map as well:
From there on there are endless possibilities:
