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I have placed a grid onto an open source Ordnance Survey map that corresponds to Ordnance Survey eastings and northings. I have a value for each grid square between zero and 30.

How do I use these values to produce a density map with 4 categories?

I am relatively new to QGIS 3.

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You want the "Graduated" symbology option.

Just choose the column the has the values and choose 4 classes.

enter image description here

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    Just a small remark: if grids are not the same size you need some normalization, e.g. "value" / $area, in case if they are the same size simply use absolute values. – Taras May 27 at 12:52

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