I am trying to place a dot and align it just in the center of the nodes of this square. But I can't make it to work properly. The thing is that nodes do snap but the result isn't exactly a nice fit in the center, as the dot is aligned to one corner.

This can be seen in the attached file.

So in other words, how can I make a sweet and nice dot aligned just in the center of the node?. Can someone help me with some video or step by step explanation?. 
Please note that in my drawing the dots are exagerated to be bigger than what they should be, I did this on purpose to better display my doubt. In reality I want them a little bit smaller. Again, how can I make those to be just in the center or in the intersection of those nodes?. Help please? Thanks.

Turn on these snap settings: Snap to cusp node, Snap to object midpoint.  

Or you can use Markers:

@Polygon

Can you make a video or gif or step by step guide of what you did?. I'm lost. Please note that my Inkscape version is 0.91 will what you did work?. What steps? Please.

Let´s see:

@Polygon

Thanks I didn't know that I could do that. It surely works on my Inkscape version.