With 2.78 we can use normal/bump map with nodes, thanks to the support of multiple tangents (commit).
It is really simple to use, just make the connection as this image shows, using new "Normal Map" node.
EDIT: you have to change Normal Map color-space to Non-Color (not sRGB), it is necessary for Blender to read Normal data. You do it in Image Editor - Color Space.
Image from Blender 2.78 Release Notes - Viewport
As your question has some images that denotes you wanted to use a BW texture (bump map), you first need to convert it to Normal Map. You can use any bump2normal conversion tool.
EDIT: the following technique is actually not possible, because Blender takes the created image as sRGB (not for Normals).
2nd technique: using the Bump_to_normal (a node group), made by Binary (don't have link) and used in the Normal Map Painter, by pachupp (I created sharedBumpMap with bump texture inside, because Bump_to_normal uses it 4 times. Changing the texture inside the group, the Bump_to_normal is refreshed).
EDIT: again, this technique does not actually work because of its color-space. It would need a new nodes setup to achieve it.
You can download the file here or (it's based on the Normal Map Painter file). In material nodes panel, the upper setup is for Bump, the lower is for Normal (yes, they look different, but it is just an example). Click on Output nodes to change the results.