In Photoshop we can display the grid, but I want this grid to be printed so I want to make the grid myself. What’s an easy way to make this?
Filter > Vanishing Point…
Set the grid size to the increments you want then double-click the Grid tool.
Then with the little preferences menu there at the top left be certain to select “Render Grids to Photoshop”.
And then just click OK.
You’ll get a grid on the document as a pixel layer. You can then change color or desaturate to get rid of the blue.
If you want the varying line weights and dotted lines, there is no easy method with Photoshop. You could however set something up in Illustrator then copy/paste to Photoshop as a Smart Object.
Edit: You can get a grid with darker major divisions by making a second grid with a Grid Size equal to some multiple of the first one (e.g. 4 to make one like in the original post). Save it to a different layer, then use layer properties (for example) to make the stroke wider or change the color.