Jewish men are expected to wear a kippa (head-covering, such as a cap or a hat) at all times. Those who are less religious wear the kippa during prayers and while learning Torah (such as when they are at a Jewish school). Non-Jews are not required to wear a kippa.
For background information:
Kippa
Yarmulke (Yiddish) or kippa (Hebrew).
Girls wear a nice dress (semi-formal) or suit to her bat mitzvah ceremony. There is no symbolism. Some girls will wear a kippa (symbolises that HaShem is always above us) and tallit (prayer shawl) if it's a Saturday morning service where they read directly from the Torah.
Most Jewish males wear a suit and tie to their Bar Mitzvah. Additionally, Jewish males are required by religious tradition to wear both the kippa and the talit.
It depends on whether you are discussing Orthodox Judaism or Liberal Judaism.Orthodox JudaismAs mentioned in the Talmud (Shabbat 156b; Kallah 1:16), Jewish males cover their heads with a kippa (skullcap) and/or a hat, as a reminder of the presence of God. The Yiddish word for kippah, "yarmulkah," is a contraction of the Aramaic "yerei malkah": to be aware of the King.Women are seen as naturally having less inclination to stray, so the custom of wearing a kippa does not obligate them.Note that Jewish married women traditionally cover their hair (Talmud, Ketubot 72b). This is for the purpose of modesty - only her husband should see her beauty - since the hair is considered beautiful (Talmud, Berakhot 24a).Liberal JudaismLiberal Jewish women are given the choice as to whether or not they wish to wear the kippa. However, any Liberal Jewish woman who chooses to wear a kippa needs to do so consistently. Additionally, any Liberal Jewish woman who chooses to wear tefillin and tallit, must wear a kippa as well. (Since Orthodox women do not wear tefillin or tallit, this is not an issue for them.)
There is no foolproof way, but often the man will wear a kippa (cap) and/or a hat, and will often (not always) have a beard.
One should be dressed modestly of course in reverence to the Torah. Other than that there is no specific obligation to wear something special. However, it is generally an accepted custom to wear a Tallit in the synagogue when reading or being called up to the Torah for an Aliyah.
Answer A man is likely to be a religious Jew if he has a kippa on (skullcap), he wears tzitzit (a 4 cornered garment with strings on the end). If that doesn't help you just ask the person. Answer Observe how he practices his religion to decide whether you think a man is a religious Jew. Does he wear the ceremonial clothing, follow the dietary restrictions, meet other Jewish men for prayer frequently, study the Torah, follow the teachings of the Torah and the books that seek to interpret it in his daily life?
The fringes or "tsitsit" (ציצית) are knotted in such a way as to symbolize the 613 commandments of the Torah. The commandment to wear fringes is in the Torah.
Answer A man is likely to be a religious Jew if he has a kippa on (skullcap), he wears tzitzit (a 4 cornered garment with strings on the end). If that doesn't help you just ask the person. Answer Observe how he practices his religion to decide whether you think a man is a religious Jew. Does he wear the ceremonial clothing, follow the dietary restrictions, meet other Jewish men for prayer frequently, study the Torah, follow the teachings of the Torah and the books that seek to interpret it in his daily life?
Formal, modest clothing.
Orthodox Jews will always wear a Kippa (Yarmulke) and/or a hat to cover their head. Others will typically wear a Kippa when they enter the synagogue or participate in other religious ceremonies.