As mentioned in that other tread, I usually use GIMP, though Piskel also does well. It would help us understand what you're trying to accomplish if you would attach the spritesheet you're working with to this topic thread.

The sprite dimensions for this sheet are not grid-aligned. They appear to be 16x16, but separate sections have different offsets, which makes this more of a "sprite-atlas" rather than a spritesheet. Can you tell me where this came from?

Ah, looks like rubberduck set them up so the overflowing tiles are adjacent. I was wrong about the offsets. It's a 16x16 spritesheet with some tiles having overflow. So, here's how to split them out into individual tiles:

1. open https://www.piskelapp.com
2. click the "create sprite" button in the upper-right corner
3. cick the folder icon "Import" along the right side
4. click the "browse images" button beneath "Import from picture"
5. navigate to your local copy of colony-other-ready.png and select/open it.
6. on the Import and Merge dialog, select "Import as Spritesheet"
7. enter a frame size of 16x16 with an offset of 0x0
8. click "import"
9. "This will replace your current animation. Are you sure you want to continue?" Yes.
10. click the mountain icon "Export" along the right side.
11. on the export dialog, find the [ Gif | PNG | Zip | Others ] tabs, select the "Zip" tab.
12. click on the "Download ZIP" button at the bottom of the dialog.
13. save your zip file somewhere you'll remember, then open and extract all the individual sprites!

Yes, that method should work for other dimensions just as well. Simply change the values you're entering on step 7. :)

As for how to determine the frame size and offset... Rubberduck explicitly listed 16x16 in the tags for this one, but it's not always so easy.

• Usually I'll pick a tile in the spritesheet with a clear border (for example, the trusses at 160,80)
• Open the spritesheet in GIMP.
• Menu bar > View > Show grid
• Menu bar > Image > Configure Grid
• Then I start adjusting the grid width and height until the grid lines seem to line up with the tiles, paying special attention to the tile I picked out earlier.

It involves some guesswork, but this method works pretty fast for me. Most spritesheets have dimensions in powers of 2, so 16x16, 32x32, 64x64 are pretty common. Often the width and height are mixed and matched, though: 16x32, 32x48. On the other hand, there's no rule that says sprites MUST be powers of two, so you'll sometimes encouter sprites with strange dimensions like 21x33. Other times, the graphics is set to conserve as much room as possible, so the sprites are not arranged in a grid (sprite-atlas) but in wherever they will fit. 

For example, this pixel dungeon spritesheet (below) has sprites in multiple sizes (16x16, 14x20, 32x32, 35x35, etc) In these cases, no amount of grid tweaking will properly slice all the sprites. Some tools like Unity have texture atlas tools that help auto-slicing the atlas, but other than that, there isn't a good easy way to do it with atlases. Just open it in gimp and start manually cutting each sprite out.

Fortunately, in this example, Zombietom uploaded all of watabou's individual spritesheets in a zip file as well, so there is no need to slice this one image manually: https://opengameart.org/content/pixel-dungeon-graphics-by-watabou