I'll join up. I'm actually building an obsidian city at the moment, so let me get a few screenshots of my current setup, to show you what I think is the best way to do it.
Edit 2: Here it is, and thanks for the spot; I appreciate it.
Alright, here we go:
When farming obsidian, there are two things that need to be kept in mind: reusibility and dwarven safety. The first in necessary to ensure profitability, the second is not necessarily needed, but most people prefer it.
To start with, make sure your magma pipe is free from fire imps and magma men, or you have a way of taking out the magma without disrupting the little buggers. This can be done with marksdwarves, or with fortifications carved into the stone next to the boarder of your magma pipe (see figure 1). Make sure you channel out your magma from above, and then seal the resulting space with a constructed floor.
Figure 1: Safe magma extraction (sideview)
___C██
__╬█≈≈
_=floor
█=unmined wall
≈=magma (unlimited source)
╬=fortification (carved)
C=channel here, then construct a floor over the empty space
Good, now you have an unlimited (I hope?) magma source free of disruptions from wildlife. Now, we need to build our actual obsidian farm. First step is to use the channel designation to dig trenches into which the magma will fill. These trenches need to be dug using the channel designation to ensure dwarven safety. I suggest each channel be two spaces wide, so that it can be designated all at once, and dwarves will be able to mine it out no matter what (see figure 2). It's also useful to connect the ends of your channels via diagonals. Dwarves can walk across diagonals, and magma can flow over diagonals. So therefore, the dwarves can walk on the level above, and magma can flow on the level below(see figure 3).
Figure 2: Obsidian-making channels (dug out)
Note how the channels are separated by a one tile wide wall. Dwarves channel from these walls.
Figure 3: Obsidian-making channels(ends)
Now that you have your channels, we need to fill them with magma. The best way to do this is by finding a narrow spot on the pipe, and simply channeling into that. Of course, if you have fire imps, that's not an option (see first paragraph). In any case you will want your infinite source magma to be separated from your obsidian-making trenches by a single tile (see figure 4) This tile has to be accessible from the level above, so you can channel it out safely. When channeled out, this will allow the magma to fill your channels(see figures 5 and 6). It is useful to note here that your obsidian farm should NOT be on the highest level of your magma pipe. Pipes take time to refill, and therefore the process is slow going if your farm is at the top. Also, forges on the top level are in danger of shutting off from low lava levels if your obsidian farm is big enough. This can result in failed moods, and therefore, dead dwarves. I suggest having your obsidian farm at levels -3 and -4, with your forges below that. Do what works best in your situation.
Figure 4: Separation of trenches and magma
Figure 5: Magma trenches filled (upper level)
Figure 6: Magma trenches filled (lower level)
Great, now that we have the magma in the trenches, we need water. The water source will have to be infinite, and therefore will be one of the following:brook/river, cave river, aquifer, or lake/ocean. Collecting rainwater in murky pools is also possible, but not recommended. The details of how to get the water from its source to the obsidian farm are left as an exercise to the reader (in the example obsidian farm, an aquifer is used; the farm is below the aquifer, so simple up stairs were enough to tap the water source). Now, once the water nears your farm, you're going to need some way to shut it off. Floodgates connected to a lever is the preferred method(see figure 7). You need these to be right next to your farm, as this will lessen the time it takes to fill the chamber, and allow for easier draining. The water should be introduced on the same level as the channeling was done, or one level above where the magma resides. This allows the water to fall on the magma, and doesn't clog up the farm. When you're ready, pull the lever and make obsidian (see figure 8).
Figure 7: Floodgates and lever blocking the water source
Figure 8: Obsidian being created
Now that your farm is making obsidian, you have a new problem. Your farm is now underwater(see figure 9). Most of your dwarves will be unable to swim, and therefore, you can't do anything with your farm. The solution: drainage. You're going to need to find some way of getting rid of all that water. There are several options available to you:
1. Pump the water back to where it came from. Any infinite source of water also has an infinite source of drainage. Simply pump the water back into the river/aquifer/ocean, and it will naturally disappear. (the example farm uses this method)
2. Chasm it. All chasms/bottomless pits can take as much as you can put into it. Add a tunnel from your farm to the chasm, and you've got drainage. Make sure you have a floodgate somewhere along the line, though, so that your water will stick around your farm long enough to make obsidian.
3. Dig out an evaporation room. When water is 1/7, it will evaporate on its own. While you could try to micromanage and pull the lever at just the right time to keep your water level low, it's never easy to do so. An evaporation chamber, separated from your farm via a floodgate (connected to a lever), will allow the water to spread out and evaporate. As a general rule of thumb, an evaporation chamber should be around 4-6 times the size of your farm, so that even in the worst case scenario (your farm fills to 7/7 water everywhere) it can still evaporate. This can be a dangerous method, though, as if the floodgates for your infinite water source are open at the same time as your floodgates into the evaporation room, you end up with a lot of water that needs to be pumped out somewhere. Still, with a little bit of attention, this is entirely preventable.
Figure 9: Flooded obsidian farm
When you start to see dry spots appearing all over your farm, and none of them are being refilled (see figure 10), it's time to harvest your obsidian. Channel out the magma filling trenches again, save for the last tile which separates the magma from the trench (see figure 11). The obsidian will appear at the bottom. An access doorway needs to be dug to the lower level of the farm, so the haulers can get to the stone. A stone door can be used to access the magma. It does NOT have to be made out of bauxite, iron, or other magma-safe materiel. So long as no dwarf steps through that door whilst magma is on the other side, it will be safe. However, if the door opens for any reason, and magma gets in the doorway, the door will melt. Lock your doors before filling the trench with magma again. In any case, stone doors can also be used to get through the walls which your dwarves channel from (see figure 12).
Figure 10: When to harvest the obsidian
Figure 11: Channeling out the obsidian
Figure 12: Access doorways
Once your haulers are done getting all the obsidian out, lock the doors and channel out the separation walls. Your trenches will fill with magma, and the process will start again.