1. Tu B'Shvat, the 15th day of the Jewish month of Shvat (sometimes written as Shevat), is a holiday also known as the New Year for Trees. The word "Tu" is not really a word; it is the number 15 in Hebrew, as if you were to call the Fourth of July "Iv July" (IV being 4 in Roman numerals).
2. Tu B'Shevat will begin this year at sundown on Monday 21 January and will end at sundown on Tuesday 22 January.
3. Judaism has several different "New Years." This is not as strange a concept as it sounds at first; in America, there is the calendar year (January-December), the school year (September-June), and many businesses have fiscal years. It's basically the same idea with the various Jewish New Years.
4. Tu B'Shevat is the new year for the purpose of calculating the age of trees for tithing. See Lev. 19:23-25, which states that fruit from trees may not be eaten during the first three years; the fourth year's fruit is for G-d, and after that, you can eat the fruit. Each tree is considered to have aged one year as of Tu B'Shevat, so if you planted a tree on Shevat 14, it begins its second year the next day, but if you plant a tree two days later, on Shevat 16, it does not reach its second year until the next Tu B'Shevat.
5. There are few formal customs or observances related to this holiday. This New Year of trees is not accompanied by a cessation of labor or specified feasting, nor is it mentioned specially in the prayers of the day. In order to make the day special and celebratory, certain supplicatory prayers are omitted.
6. It is customary to eat the fruits associated with the Land of Israel (dates, olives, figs, and pomegranates), and to partake of some new fruit not eaten yet that year, if available. The fruits associated with the Land of Israel are enumerated in Deuteronomy 8:8: "...a land of wheat and barley and (grape) vines and fig trees and pomegranates, a land of olive trees and (date) honey" (Deut. 8:8).
7. In Israel, it is customary (especially for children) to plant new saplings or plants on Tu B'Shvat. Jews living outside of Israel often commemorate the holiday by donating money to the Jewish National Fund (the traditional "blue boxes") to plant a tree in Israel.
8. Another long standing custom (among the religious apparently, I've never heard of it) is to pray at this time for an especially beautiful etrog (citron) for the next holiday of Sukkot.
9. Some people have adopted a "Tu B'shvat Seder" for the evening of Tu B'shvat, based upon the writings of the students of the Arizal in the book "Pri Aitz Hadar" ("citrus fruits"). The holiday is celebrated with a "seder" analogous to the Passover night seder, and indeed the night marks the beginning of a 60 day period until Passover.
10. You can an explanation of how to perform this Tu B'shvat seder here.
11. My kids have had a Tu B'Shvat seder in preschool some years, but it's not something we've ever done at home.
12. CafePress apparently sells Tu B'Shvat t-shirts. Who'da thunk it. (Yes, I'm reaching a bit here...)
13. Tu B'Shvat coloring pages and games can be found here.