Welcome to the daily halacha (Jewish law). Maran (our master) HaShulchan Aruch, Orach Chaim, siman (section) tzadi (Hebrew letter) chet (Hebrew letter). The person should be careful to wear proper, mechubad clothing, respectful clothing for tefillah (praying).
One of the most famous questions that comes up is: In the summertime, can a person pray in shorts? Halachically, no. Can a person pray in a shirt that is not so respectful and modest—one that is a little too open, maybe a little too short on the arms? When it comes to shirts that do not cover all the way to the palm, halachically, that is fine. But a person should not be chazan (cantor) without wearing a proper long shirt that covers the whole hand, the whole arm, and the whole stomach.
Could he pray by himself, the amida (standing prayer), with such a shirt? Yes, there is room to be lenient, as long as his body is obviously covered, even though his arms are not fully covered. But can a person pray in shorts? Halachically, a person cannot.
Yalkut Yosef says that if a person is not feeling well, cannot leave the house, and can barely get dressed, then in such a situation, a person can even pray in pajamas. Otherwise, Yalkut Yosef says that a person cannot be lenient and pray the amida, Shacharit (morning prayer), Mincha (afternoon prayer), or Arvit (evening prayer) in shorts or a short-sleeved shirt. And even if they are going to be lenient and pray in a short-sleeved shirt, they should never be chazan; they are not dressed modestly for tefillah.