We are actually never given a physical description of Romeo. However, we may be able to infer a few things about his appearance from the text. We know that his father is a Lord because his mother is referred to as Lady Montague and also because the opening Prologue describes the Capulet and Montague families as being "alike in dignity" (Prologue, 1). The term "dignity" can be translated as "rank" ("Romeo and Juliet," shakespeare-navigators.com). The word rank(it) refers to their social, or noble, status. Hence, we know that Romeo is fairly rich and probably fairly richly attired.
We are never directly told Romeo's age like we are told Juliet's; however, we can guess that he is in his late teens or possibly early twenties because these are the ages in which he might be considered a young man. We know from Friar Laurence that he can be considered a young man, as we see from his lines, "Young men's love then lies / Not truly in their hearts, but in their eyes" (II.iii.68-69).
Another thing we can infer about Romeo's appearance from the text is that he is very handsome. We especially learn from the Nurse that he is very handsome when Nurse describes the beauty of Romeo's face and body in saying:
[T]hough his face be better than any man's, yet his leg excels all men's; and for a hand, and a foot, and a body, though they be not to be talked on, yet they are past compare. (II.v.39-43)
Hence, we can infer from the text that Romeo's appearance can be described as being a well-dressed, young nobleman who is very handsome.