How to join vertices of two objects Is there is more automated and accurate way to connect two vertices of neighbouring objects?

I tried to move them manually, but it is a bit difficult to do it just in point.

I'd like to make flat and smooth faces for the bottom and sides. The top face is going to climb a bit to align with vertices of the other - higher object...
You can use Snap during transform tool set to Vertex.

Then you can snap directly one point to another or just choosen axis for example G > Z then hover desired vertices.

And if you want to trully connect them then you should have meshes joined and after Snap hit W and Remove Doubles.