The Pan tool in Paint.NET is the most simple tool on offer within the Tools palette. It does one very basic job and offers no options within the Tool Options bar that may adapt how it operates. It just allows you to move or pan the page when you have zoomed into it.
To use it, you just select it from the Tools palette or press the H key on your keyboard and then click and drag the page to pan it from side to side or up and down. If the page isn't zoomed in when the Pan tool is selected, a small cross will appear beside the hand cursor icon that indicates that the tool cannot be used.
Alternatives to the Pan Tool
There are a couple of alternative ways to move a page around, other than using the Pan tool. The first is quite obvious and requires using the scroll bars that are displayed to the right and bottom of the page. The second is not so obvious, but will be familiar to Adobe Illustrator users. You can hold down the Space Bar and you'll see that the cursor icon changes to a hand and you can now drag the page around in the same way as if you had selected the Pan tool.
There are a couple of things to note when using the Space Bar keyboard shortcut. Firstly, remember that as soon as you release the Space Bar, the icon changes back to the currently selected tool and the panning action stops. Secondly, you can't use the shortcut if the Text tool is the active tool as you'll just add a lot of spaces to whatever text you were writing.
The Pan tool is an essential tool for when you have zoomed into a document, but personal choice will dictate whether you select the tool or just use the Space Bar shortcut or scroll bars when you need to pan the page.