As was stated in another message, Sphagnum Moss is harvested from live plants and dried. Peat is the partially decomposed sphagnum substrate beneath the moss in the bog.
Some folks use sphagnum on tank bottoms as cover and for collecting eggs. I know of one killie nut who uses it instead of the requisite nylon/acrylic yarn breeding mops. Others use it in a "natural" setup with tons of surface plants, such as Water Sprite, so they don't bother with collecting eggs. The fry have plenty of hiding places.
Soak the moss in an empty tank for a few days first to get it to sink. There is often a bacteria bloom where the water turns a milky white. You can introduce the fish after the spike. Folks use primarily live food, such as brine shrimp and black worms, in these setup to reduce fouling from uneaten flake or pellet food. Depending upon your water conditions, temp, etc., the moss can last about 6 months before it starts to decompose and should be dumped.
As others have pointed out, peat is what most folks use to condition their water. It can be added by placing it in an old nylon stocking, in a mechanical filtration container/cartridge, or in a corner box filter with floss or poly-fill on top to keep it in place.
Others will use it in a separate container to condition their change water, sort of a black water tea. Some will place a stocking full in a plastic garbage can or similar container. One person I know fills the bottom with loose peat and runs an air stone at the bottom to keep the water "sweet." Otherwise the peat will continue to decompose and become foul at the bottom. This person mixes the water with tap water to reach his desired target pH. He also breeds annual killies and will reach in and grab a handfull or two for the bottom of his breeding tanks. As the supply becomes low, he starts a second can.
Both sphagnum and peat will soften the water and drop the pH. Peat will do so faster and to a greater degree as it's "concentrated."
Also, regarding ammonia spikes, naturally occuring ammonia from fish respiration and waste becomes more hazardous. There's a reason for this based on tank chemistry. The killie list had an exhaustive, and sometimes confusing, discussion on this topic a while back ago. Here's a link to an archived message in the middle of the thread that's interesting.
The key, as far as I understand (and I'm not a chemist), is that when the pH drops to 6.5 and lower, the biofilter's ability to naturaly rid the water of harmfull ammonia ceases. But the fish keep adding to it via respiration and waste.
The bottom line is that the lower the pH, the more often you need to change the water in order to rid it of harmfull ammonia. This is even more critical to fry as the damage to gills from ammonia is permanent and will stunt or kill them off. Adult fish may recovere once the water conditions improve and the damage is not too great.