Asara Bi'teves is a fast day but as we know fast days are often anything but fast. I don't get the sense that anybody seems to be particularly sad or down on this day [unless dating isn't going well or parnassa is rough]. So a few suggestions to make the day count.
1] Read about it.
2] Pay attention to the meaning of the words when you say slichos. Slichos are meant to create a mood.
3] The Chief Rabbinate made this day Yom Hashoah so reading and thinking about the holocaust is worthwhile [as it always is].
4] Fast days are for teshuva. I can imagine we all have things to fix.
5] Tzedaka. כי קרובה ישועתי לבוא וצדקתי להגלות. The redemption will be in the merit of tzedaka.
6] Think about the Beis Hamikdash and what we are missing [if you don't know you can learn about it].
7] Listen to shiurim about the day [you can listen on kol halashon.com and I assume on yutorah.org as well].
8] When you break the fast try to have kavana when you make a bracha on the food.
The fast is a means to an end. The end is returning to Hashem.
Love, blessings and an easy, fast, meaningful fast.
Thanks to A.R.L. who inspired this post.