Set up a time to talk to your family about the Rebbe, his life, and his inspiration and impact on the world, hastening the geulah.
If you are able, visit local shuls and batei midrashos. When there, share a vort from the Rebbe, explain how he loved every Jew, and tell them about the horaos he gave us. If possible, all this should be done in the course of a farbrengen.
If you can, visit youth—both observant and, wherever possible, the not-yet-observant—and talk to them about the great affection the Rebbe had for them and the hope he placed in them as future propagators of Torah and Yiddishkeit.
Where appropriate, the relevant horaos for the yom hilula (see above) should be continued in the subsequent days as well.
Kiddush Levanah
According to Kabbalah, the earliest time to recite kiddush levanah is the seventh day from the molad, i.e., Wednesday night.