The facts about Holga apertures
The commonly cited [1, 2, 3, 4, 5, 6, 7, etc.] stock Holga apertures of f/8 and f/11 are bullshit. You only get one, and it's about f/13.
Here's why you only get one aperture: yes, there is a switch with sunny and cloudy icons on it, and when you slide it, it moves a little arm inside with a hole in it. Unfortunately, the hole in the arm that's supposed to make the aperture smaller for the sunny setting is larger than the smallest hole in the light path, so the switch makes no difference.
Fig. A: the hole in the aperture arm doesn't let any less light in
The shiny bit inside the circle inside the rectangular hole in the aperture arm is the back of the lens. The circle around it is the smallest opening in the light path from lens to film, regardless of the position of the aperture switch. This means that it alone determines the f/stop value.
An f/stop is the ratio of the diameter of the aperture to the focal length of the lens. For example, for an aperture with a diameter of 25mm on a 50mm lens, you have a ratio of 50:25, or 1:2 (which is how it's often written on lenses) (50 ÷ 25 = 2), or f/2.
Fig. B: the smallest aperture on the back of the lens with a metric ruler
Here's why it's about f/13: while it's not exact, I think we can safely call this 4.5mm in diameter. If we believe the Holga about the focal length of the lens being 60mm, we can now calculate the real f/stop: 60 ÷ 4.5 = 13.333, or about f/13. There you have it.
Modifications
Fig. C: the back of the lens with the smallest ring removed
If you want to change it, you can pop that little ring out very easily with a pen or small screwdriver, which, as you can see above, will leave you with an aperture of 6mm, or f/10. That's only 2/3 of a stop, which is within the exposure lattitude of most black and white and color print film, but a bigger aperture will generally vignette more. And hey, 2/3 of a stop is 2/3 of a stop.
You can also glue the ring that you popped out over the hole in the arm, which will give you a selection of f/13-ish on the sunny setting and f/10 on cloudy. Or you can fill in the hole on the arm and drill it to whatever you want.
Other uses for the aperture arm
As Mark Beltran suggested, you can put a red (or whatever color) filter on the hole in the aperture arm. You can also do an infrared filter (info from Andrew Davidhazy on how to make your own), diffusion material, a thin maginifying optic (make sure there's enough clearance when you screw the shutter plate back on), or remove the lens stop screw so you can take the lens off and install a pinhole. You can then switch whichever of these you install on or off.
Maximum aperture without drilling metal
Fig. D: shutter dimension 1: 6mm (slight parallax here, it's 6)
Fig. E: shutter dimension 2: 7.5mm
The hole in the shutter plate is 6mm x 7.5mm, so this determines the maximum aperture you can get without drilling metal (the rest is plastic, and while annoying and potentially dangerous, can be modified with a sharp knife). Since the opening in the shutter plate is rectangular, we'll have to go by area.
Math review: the formula for the area of a rectangle is a = width x height, and the formula for the area of a circle is a = πr², where r is the radius (half the diameter).
The area of the shutter plate hole is 45 square mm (6mm x 7.5mm = 45mm). Now we need to figure out what the diameter of a circle is that has an area of 45mm: er, since I can't seem to figure out how to solve for a right now, I took an advanced limited linear programming approach and punched radii into my calculator until I got something that was close enough (that's right, I've got skills). A radius of 3.785 yields an area of 45.0072 square mm, so that gives us a circle with a diameter of 7.57mm, or approximately f/7.9 (radius of 3.785mm x 2 = diameter of 7.57mm, and focal length of 60mm ÷ 7.57mm = f/7.9). The moral of this bit is that if you want a aperture greater than that, you have to drill the metal shutter plate and shutter disc.
