How do people greet each other on Lag B’omer? For example, on a festival, one would say חג שמח. Is there an improper way (according to Halacha) to do so?
The traditional formula for the day is "Today is thirty-three days, which is four weeks and five days, of the omer."
This is not actually a greeting, but the Shulchan Aruch (Orach Chayim 489:4) specifically recommends not saying "today is x days" before counting the omer with a blessing, because by doing that you fulfill your obligation and can no longer say a blessing before counting it. It would follow that using "today is thirty-three days" could potentially be an improper way to greet someone.
Obviously this doesn't mean that you can't use "today is thirty-three days" as a greeting, but that if you do so for the first time that day, you should say it with a blessing, with the intent to fulfill the commandment, and with the number of weeks in order to fulfill the commandment in the best possible way.