Fitting a brewer's airlock into the lid of a Mason jar is another quick and easy modification that turns the jar into a fermentation chamber. The airlock is a little plastic device with a volume of water in it, such that CO2 can pass out through it, but no air can come back in. This lets you set your pickles, beer, or whatnot to fermenting and allows them to emit carbon dioxide smoothly without letting in outside contamination.
Below is my recipe for a fermented hot sauce, in the style of Tabasco (Tabasco ferments for three years in oak barrels).
1. Punch a round hole in a Mason jar lid, 1 centimeter in diameter, to accommodate your airlock.
2. Wash, halve, and remove stems from a volume of hot peppers that will fit into your jar. I use half-gallon jars, and red (ripe) jalapeno peppers, or rocoto peppers, or infinity peppers if I'm making it for an enemy. Use proper pepper-handling techniques at all times.
3. Weigh the empty jar.
4. Put the peppers in the jar, and fill with warmish water almost up to the level of the peppers.
5. Weigh again, and calculate the net weight of peppers and water.
6. Add to the jar a weight of non-iodized salt equal to 5 percent of the weight of the peppers and water. In a half-gallon jar, this will be about 5 tablespoons of salt.
7. Add a tablespoon of plain yogurt, to inoculate the jar with Lactobacillus. Adding a peeled clove of garlic for flavor is optional.
8. Put a non-holed lid on the jar and shake it to distribute and dissolve the salt.
9. Replace the lid with the prepared one. Fill the airlock with water and insert the airlock into the hole in the lid, where it should just perch snugly.
10. Leave the jar on a shelf for 4-6 weeks. The airlock should bubble occasionally as the bacteria excrete CO2
11. Open the jar and carefully drain the liquid out into a separate container, like another Mason jar.
12. Puree the pickled peppers in a blender, adding back in some of the liquid to achieve the consistency you want, and adding vinegar -- sherry vinegar is excellent -- to increase tang if desired.
13. Optionally, while it's spinning in the blender, mix in 0.1 percent by weight of xanthan gum to reduce syneresis (a.k.a., separation of the liquid from the solids).
14. Bottle, store in the fridge, and enjoy. The reserved brine can be used to make a new batch of pickles.
Sandor Ellix Katz is a great resource about delicious home fermentation.
The NCHFP is an excellent source for information on safe canning practices -- and it's important to note that they have no recommendation for canning mashed potatoes, even in a pressure canner. Other dense purees like pumpkin and sweet potato, are expressly not recommended for canning, as the density can prevent adequate heat penetration to ensure safety. I would not can mashed potatoes under any circumstances.