If the boy and girl who are to marry are present in the meeting of nikah then there is no need of appointing a wakeel. Yes, in case any of the two is not present in the meeting of nikah due to any reason then he or she has to appoint a wakeel who will either put offer of nikah or will accept it; since the offer of nikah and its acceptance is to be made in single meeting.
A wakeel of nikah should be one who is trusted. While appointing him wakeel you should say: “Get me married to that person.” If he accepts this offer he will be your wakeel. Generally, the qazi becomes wakeel from girl who acts with permission of the girl or her wali (guardian).
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband