How do we celebrate the 15th of Shebat today?
There are no Halakhic instructions for any celebration of T"U Bishbat. The custom in many communities is to eat at night or during the day all type of fruits, and especially the seven fruits or species by which the Land of Israel was praised in the Tora: "...a land of wheat and barley, grape and fig and pomegranate; a land of olives and honey (=dates)" (Deut. 8:8).
Certain families have the custom to organize a Seder of T"U Bishbat. Saying berakhot ha'ets for the fruits of the tree and the correspondent berakha for whatever else is eaten, like wheat, barley (normally mezonot), etc. Many consider a special zekhut to have for this Seder fruits from the Land of Israel and say berakha for them.
No special prayers are added to the regular services today. Tahanun, however, is not recited in T"U Bishbat.