For example, select the largest possible grid which can represent all needed coordinate points (in your case 1 mm would be good). Go to the zero point (your reference). Press spacebar. Select the item for moving so that you grab it from the center point. Move it while looking at the dx and dy coordinates in the bottom status bar of the view. Drop it to the wanted coordinates.
Or, again using the “local origin” with the spacebar. Select the item and use context menu → Positioning Tools → Position Relative to… and Use Local Origin as the reference. Write the coordinates, OK.
In my personal working method, I try to incorporate (127, 127) as an “important” coordinate on the PCB. It can be a fiducial, pin 1 of a THT connector (preferable) or else some other part. It could even be the corner of a PCB, but those are less well defined during PCB production and I tend to avoid doing that. I use (127, 127) because it’s also 5 banana units, so whether you align things to absolute (0, 0) or (127, 127) and either metric or banana units, it gives you the most chance of keeping all your grids aligned with each other.
PCB outline I usually draw on a metric grid. I am living in (mostly) civilized Europe, and we agreed upon length measurements some 200 years ago. THT connectors ans other footprints I usually place on a 100mil grid, to maintain breadboard compatibility. The atrocious arduino kludge would never occur for me. I’d rather throw the boards away and respin the boards. Mounting holes depend on the situation. Sometimes it’s convenient to drill existing holes in matrix PCB bigger, and then I put the holes on a 100mil grid. In other situations I keep things metric and in whole mm for anything mechanical.
eelik already mentioned the space bar to reset relative coordinates, and Context menu / Positioning Tools / Position Relative To. Another method is to select your hole (or hover over it, and press e to edit it’s coordinates. You can then directly enter numbers or simple formula’s in the entry boxes either in the properties window of your hole, or in the properties manager on the left side of the screen (if that is enabled).