משנכנס אדר מרבים בשמחה- When Adar Begins we increase our Joy (I know it is not in Shulchan Aruch or the Rambam) What is the practical application of it?
Chasam Sofer says that it has little or no practical application, and indeed he says that this is why Rambam and Shulchan Aruch don't cite it as practical halachah.
However, the Minchas Elazar (Nimukei Orach Chaim 686:1) raises several objections against the Chasam Sofer's position. He writes (quoting his own statement in another of his sefarim):
אבל משנכנס אדר מרבין בשמחה נקט סתם כי מדה טובה מרובה, ובאיזה דבר שנוכל אז להרבות בשמחה מצוה איכא, וכל אחד ישער בלבבו ונפשו... מצוה בכל מה דאפשר להרבות בלבו ובעניניו בשמחה של מצוה ולקיים דברי חכמים
"But it just says 'when Adar begins we increase our joy' without further specification, because the good aspect is greater [than the "decrease in joy" during Av, for which specific areas are mentioned]. So whatever we can do to increase in joy - there is a mitzvah in doing so, and each person has to evaluate this according to his own heart and soul... It is a mitzvah, insofar as possible, to increase the mitzvah-related joy in his heart and in his affairs, and to fulfill the words of the Sages."
(.בבלי תענית כט) is the source of this verse. One possible application is mentioned in Mishna Berura 686.8 that if a person has a court case it is best if he can push it off till Adar. By winning the court case it definately adds Simcha.
One can most effectively increase joy in Adar by increasing the joy of others. Hence the Mitzvah of giving money to the needy and giving gifts to members of your community, with preference for those individuals that you have trouble getting along with! Imagine the world we can live in, if our truest, highest joy comes from the radiant faces of those we bring joy to...
If it is understood as an instruction I would assume one should be happier in Adar than one was in Sh'vat.
If, on the other hand, it is merely a description of the state of affairs in Adar than perhaps it describes the fact that people are happier in Adar than they are in Sh'vat.
Chabad.org suggests that we can increase our joy mentally. That is, during Adar we should do our best to take everything optimistically, feel happy, be happy with what we have and "not kvetch."
While we should be constantly doing this, Adar is a month when we should be trying especially hard to be happy in everything we do.
There are also likely practical ways which was perhaps the original intent of the question.
Revach.net quotes the Nimukei Orach Chaim from Piskei Tshuvos 686 footnote 17, who learns that, as they put it:
...anything we can do to increase our happiness is a kiyum of the mitzva.
Because this Mitzva has no concrete guidelines and depends on the nature of each individual, says the Nimukei Orach Chaim, the Rambam and Shulchan Aruch do not bring it. They only bring Halachos with concrete manifestations, which include aveilus in Av, but not happiness in Adar.