The Basics: Stockpiling means simply purchasing and storing a year's worth of of an item (toothpaste for example) as opposed to buying the item as you run out of it. There are many items that you use on a daily or weekly basis--toothpaste, toilet paper, food stuffs--so it makes sense to stockpile these items on an annual basis as they come on sale. Stockpiling allows you to always have a supply of needed items on hand, allows you a hedge against price increases, and precludes the necessity of running out to the store either when you run out of an item or when a major storm is headed your way. Many people have also found their stockpile of supplies can carry them through times of job loss, injury, or illness.
What to Stockpile: Make a list of the items that your family uses on a regular basis. My list includes soap, shampoo, toothbrushes, toothpaste, razors, toilet paper, cleaning products, laundry soap, paper towels, dryer sheets, hair products, feminine hygiene products, canned foods, rice, beans, etc. Now figure out how much of each item your family would use over the period of a year and buy that much of each item. If you look on the storage shelf in my garage you will find 25 tubes of toothpaste; an adequate amount for our family for one year.
When to Stockpile: Immediately. If finances are a limiting factor, consider picking one item and stocking a year's worth of that product now. Next week or next payday, choose another product and do the same. Some people stockpile all of the items on their list at the beginning of each year while others stockpile as each item on their list comes on sale. Whichever method you choose, it is important to being this project immediately.
Considerations: Space will be your primary consideration when stockpiling. Think of ways to store the items (in the garage, under beds, in a closet, etc.) that will make them both easy to access and easy to inventory. You will also want to be able to rotate the products so that "first in" is "first out". You will also need to ensure that your stockpile is protected from extreme temperature, humidity and rodents. Obviously, if you move often, have extremely limited space, or extremely limited finances, you will have to adjust your stockpiling strategy accordingly.
Stockpiling isn't only for extremists. It is a valuable, common-sense way to ensure an affordable, steady supply of the items you use most often and is one of the cornerstones of preparedness.