Dear Friend,

The covering of one’s head is both a mitzvah b’Rabbonon…rabbinic rule as well as a Minhag h’Avinu (the custom of your father).

In modern times, with some reasonable exceptions, most, if not all, followers of Orthodox Judaism, wear either a hat or a kipa at all times that they are “awake”.
Sometimes, a baseball cap is worn instead. Conservative Judaism, for the most part, requires a head covering only for prayer and eating/drinking but some do cover their heads all the time. Reform Judaism, as far as I know, has no rules concerning covering the head…some do while others don’t…even in prayer.

The “minhag h’avinu”…the custom of your father means that you are bound to do as did your father before you. If he wore a kipa all the time, so do you. If he did not, you don’t either. There does exist a question with regard to minhag h’avinu that I will address in the next question.