Eating this delicacy is an excellent way to calm a stomach upset from eating too much delicious Japanese cuisine.
Pickled ginger comes in two varieties: Gari (ガリ) and Beni shōga (紅生姜). Both are examples of tsukemono and used as condiments.
For Beni shōga, the ginger is cut into thin strips, dyed red then pickled in umeboshi. This is the traditional accompaniment for gyūdon, okonomiyaki, and yakisoba.
Because sushi is the most popular form of Japanese cuisine, more people are familiar with gari, which is also called "sushi ginger". Gari is thinly sliced young ginger that is marinated in sugar and vinegar.
You can make this yourself if you don't like consuming the artificial dyes in the commercial varieties. Take two pounds of young, fresh ginger, slice thinly and rub two teaspoons of salt over the pieces. Let them soak in the salt for an hour in a bowl then pat dry with a paper towel. Transfer the ginger to a sterilized heat resistant container. Bring sugar and vinegar to a boil (in a 2 cup to 3 cup ratio) until sugar has dissolved fully. Pour this over the ginger and allow to cool on your counter.
If the ginger is old, it will turn a pale yellow. Cover the jar and refrigerate.
Beni shōga is arguably more healthful of the two forms of pickled ginger in that it contains umeboshi. Both are an excellent way to cleanse the palate.