Need more powerful tools?
The simplest option is to share the PDF to Apple’s Notes program.
Here are the steps to bring a graph paper into Apple Notes:
Complete the transfer to Notes --
Of course you can use any drawing app that can import and edit a PDF. Choosing a full-fledged graphic design program will give you more capabilities than Notes. One app we like and use is Graphic for iPad. It has an amazing amount of power for not much money and also works with an Apple Pencil. It has features like 'snapping to grid lines' that makes adding shapes easier. Also, Graphic for iPad can add lines, notes or even modify the shapes originally created in our app, for example, and even change line color or width.
Coloring a grid using Graphic for iPad
[Also available for the Apple Mac]
PS. We have no association with Graphic other than we use it.
When you export a PDF to Graphic, have Graphic “Import as Vector Objects”. Now you can add lines/text on top, and you have access to all the lines in the drawing. So, for example, in the image below, you can grab a section of the grid and change the colors of the lines in that section. One can also change line weights - or get crazy and add arrows or dashes. One can even grab and move things around on the page.
Another helpful feature is “Smart Guides” that will snap to the grid lines on the paper rather than Graphic’s internal grid points - which probably will not match up. This should make it easier to draw on your own lines - particularly with an Apple pencil.