I think that an easy way to begin eating fermented foods is to try to start each meal (well at least your evening meal..), with Sauerkraut. We take a small bowl before our meal - kind of like a salad - because you don't need much but it will help your digestion and keep your stomach juices working well. Start with sauerkraut, and then you can move on to other vegetables, I also like pickled Daikon or pickles cucumbers... etc.
Recently, on NPR's Fresh Air, Sandor Katz was the guest and does a great job explaining fermented foods. He should know, he wrote the book, The Art of Fermentation. He reviews the healthfulness and also hands out some great recipes, so that you can make pickles and other fermented foods in your own kitchen. He gives a recipe to make your own sauerkraut which is (or click on the NPR link to get the FULL recipe):
For fermentation newbies, Katz recommends starting with sauerkraut because it's particularly easy to make. To begin, take a cabbage and any additional vegetables you want and chop it up. Put your chopped veggies in a large bowl and lightly salt them. (Katz notes that he never measures the salt because there's really no "magic number for how much salt to use.")
After salting the veggies, which helps get rid of excess water, Katz squeezes them for a few minutes to release their juices, so that they can be submerged under their own liquid. (Katz says he hardly ever adds water to his kraut, because the flavor is more concentrated if you use only the vegetable juice.) He then stuffs the veggies and the juices they've released into a jar.
"You want to press really hard to force out any air bubbles," he notes. "And you want to make sure that the vegetables are pressed down under their juices. And then just seal the jar — but be aware that pressure will be produced, so you don't want to leave it for days and days."
Katz recommends checking the jar on a daily basis to release the pressure — and then after maybe 3-5 days, enjoying your new creation.
If this is too much for you, maybe to start with you can buy some, and then after you get used to it you can make your own... we like Bubbies brand or Real Pickles brand sauerkraut both are delicious and stay away from using sugar, which defeats the purpose of pickling (which maybe becomes more of an alcoholic beverage, with the addition of yeast!?), it should really just be salt in the fermenting process and maybe some 'secret' flavors like Juniper berries, peppercorns etc... But back to the purpose here... Start easy and help your family be more healthy and happy by introducing pickled vegetables into your daily routine.
If you like spicy things and you are ready to move to the next level Kimchi is delicious! You can usually find local brands in your local health food store.
Listen to NPR's Fresh Air conversation with Sandor Katz
Listen to Part II on NPR which talks about Edible Fermentables: Wine, Beer, Cheese, Meat