Peat filtration. Peat also softens water slightly, and the way it does this has the effect of reducing the pH in moderately soft water, say <50 ppm CaCO3 The complicated and heavy organic molecules of humic substances in peat bind some of the water's positively-charged divalent calcium (Ca++) and magnesium (Mg++) ions responsible for "hardness" and exchange them for positively-charged hydrogen (H+) ions. The more free H+ ions, the lower the pH, by definition. However, if your water is hard to begin with, say >100 ppm CaCO3, its carbonates will keep the pH buffered, and the mild softening effect produced by peat in the filter won't ever result in Amazonian blackwater. Rainwater is the answer there.
Peat filtration is also a convenient source of soluble polyphenols and humic substances. Peatwater is one of my substitutes for handy commercially produced "blackwater extracts." Others are leaf litter slowly breaking down in the aquarium, perhaps including a Ketapang (Terminalia catappa) leaf or two substituting for the less-renewable Osmunda fiber that's hard to come by now, or coconut shells, even a used green tea bag in the filter.
What kind of peat to use? Don't be dissuaded from buying the plain inexpensive unprocessed Sphagnum peat moss (you won't confuse it with decorative Sphagnum moss itself) that comes packaged in small compressed bales at your garden center. Better check the labelling to make sure it doesn't have any fertilizers or other additives contaminating it. You can be sure that any added ingredients will be featured in large letters on the packaging as a selling point. There is no difference between rough-cut garden-center peat with a few twigs still in it and sieved peat compressed into tidy little pellets and packaged for the aquarium hobby —except in the price.
If you purchase aquarium-processed peat from Fluval, Eheim, Aquatronics, or Marc Weiss, you will not have any problems with too much or too little peat. These compressed peat pellets are also sieved to eliminate all but the larger granular or fibrous materials, which won't blow around in your water. I've always used peat right in a bag in the filter, but I have very soft water and smallish tanks, and I can measure the amount of peat I need in soupspoons. You might tie up a bag made from the toe of a nylon stocking, set "upstream" of the main particulate filter, which will trap any stray peat fibers.
Pre-wet the peat. When it's bone dry, peat can resist wetting; so, pouring boiling water once over the peat first helps wet it and control it. If you have any hesitation about the peat constantly in the filter becoming too strong, pour boiling water over it and let it steep it overnight, and add the "tea" instead.
In general, stability of the pH is more important to fish than any particular pH value. Don't rush too fast to add more peat: use a little, then test it and wait a day. You should avoid making changes greater than 0.2pH in a day. Keep a log.
I keep moist peat in a big plastic funnel, set over a large jug. When I first fill the funnel with briefly-boiled peat moss, the initial couple of jugfuls dribble through a little too quickly, and I have to give them another pass. But soon the peat fibers swell and settle down and clog up, so that peat-water dribbles and drips through overnight. It's enough golden peatwater for my apartment-scale needs. I only need to pour boiling water over the peat one first time and steep it like tea. After that I can just keep it wet by passing water through it every few days.
By the way, maybe you should avoid aluminum pots if you're actually boiling peat. The peat's acidity could release toxic aluminum ions. Stainless steel is safe. Pyrex or enamel pots are even better choices.
"Spent" peat. Peat is "spent" when it has adsorbed as much Ca and Mg as it's going to. Peat should be renewed if the pH begins a gradual increase over a week or so, rising toward your normal pH value. This is a sign that the peat in the filter is "exhausted" and should be put out to pasture.
At first your water tests will give you an idea when the peat filter isn't working any more. Then you'll just get the feel of it. But the color of the water isn't a dependable indication. You may find that even clear peat filtrate is still softened enough for your purposes.
Try to use your "spent" peat in repotting houseplants or in your garden, or culture Grindal worms in it, if you can't get coir. If you're setting up a new aquarium, spent peat, with its acidity neutralized, can also be an excellent source of humus, when you've mixed it with a light hand into the lower part of your substrate, where plant roots will run. In the garden it's a great conditioner, adding texture and water-retaining humus to any soil, and the adsorbed calcium and magnesium it gained in aquarium use will help counteract its natural acidity.
Use a low-ash activated carbon to remove any resulting tannic color from the water. The lower ash carbon does not affect the pH. But don't combine carbon and peat filtration at the same time: the two are working at cross purposes. Alternate them, if the amber color of tannins that peat releases into the water offends you. First let the peat do all the softening it can, and then remove tannins with carbon.
Burningham's Peat Bucket. In highly buffered, alkaline water you won't get any appreciable softening with spoonfuls of peat in the filter. You need a whole bucket of peat. Englishman Mark Burningham really takes the bull by the horns. His peat filtration technique doesn't measure out mini-pellets of specially-packaged sieved peat one tablespoon at a time. He's taken a thoroughly rinsed new five-gallon plastic bucket and drilled a hole in the bottom, about a centimeter in diameter. Then he's covered the base of the bucket in an inch-or-so layer of filter floss. Over it he adds ordinary unadulterated baled peat moss from a garden supply center, enough to fill the bucket three-quarters full. He sets the bucket on a pair of wood slats over a large drum and pours enough boiling water through one time, to just wet the peat. He lets the resulting peat tea drain off into the garden, but if you wanted the tannin and didn't plan to use the water right away, I'd think it was fine for the aquarium. Then Mark just keeps refilling the bucket whenever he thinks of it. His fuller description, with photos is at his site.
Niels Jensen, aka Tim Bo, has written a full account of the uses of peat water in the aquarium. Jorgen Scheel, the killifish guru, has also written about the uses of peat water in the aquarium.
Peat filtration beds in wastewater management. Today's new wastewater technology has often been adapted for tomorrow's aquarium filtration, so you might be interested in the details of peat filtration beds. In the domestic wastewater management field, peat fibers are being used as a kind of filtering substrate: beds of compressed peat, lightly buried in concrete or plastic containers, have been used lately to treat domestic wastewater effluent as it leaves septic tank systems. Two rival companies have been particularly involved in this technology; one, the Irish national peat board, Bord na Mona (ANUA in the US), call their system "Puraflo;" the other, a Maine-based company, touts its rival "Enviro-pure" system, one of two systems described by the Barnstable County Department of Health and Environment. You might also want to see the University of Minnesota Extension Service report on peat filters.