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.
Creating Graph with Pattern
It will look something like this.