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I have a task where I need find the density of building footprints. I have a vector layer consisting of building footprints in polygons.

To find the density I was thinking about drawing a set of squares and then make QGIS calculate how many polygons are within each square and then color them according to that number, for example from black to white, where black would be the highest density, and white the lowest. If a polygon occurs in two or more squares it should be included in the one where most of the polygon is present.

I hope some of you have any knowledge regarding the task, and perhaps a step by step idea on how to do it, as I have very limited technical skills in QGIS.

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Your approach have some problems. Creating a grid for calculating density could be wrong, because the dimension (and position) of the grid changes the density (if a group o buildings falls inside two squares it takes a density, but the density is completly different if all the buildings are inside one square).

So I suggest to create a heatmap using centroids of your buildings (Vectro->Geometry Tools->Polygon Centroids).

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