I've seen this effect on several sites, basically it's just a simple background with a bunch of dots, and I'd like to use this for a background for something but I don't know where to start!
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To get a repeating pattern like dots, you want to use the Fill tool with its pattern option. You will probably want to create your own pattern rather than use the built-in ones. One way to do this is to use the "clipboard" pattern, that is, the pattern choice in the pattern option list that is labeled "clipboard". To select this mode, click on the pattern square, and select the "clipboard" pattern, which is either labeled that (in list display mode) or is the upper left square (in the pattern array display mode). Leave it in that mode.
You then need to construct your pattern, say in a 4x6 pixel rectangle for the small pattern in your example. You need to select this 4x6 area in some window. Switch to the fill tool in pattern-clipboard mode and control-C to copy your selected area onto the clipboard, which will simultaneously put it into the fill pattern square. You can then fill as much area as you want with your dots.