What is the proper procedure for the repetition of Shemoneh Esrei - to sit or stand? I see people doing both.

Shalom, The Rema in his additions to the Shulchan Aruch (O.H. 144,4) writes "Some say that all the congregation stand during the repetition of the Amidah by the Chazzan". The Mishna Brurah there explains that as the Chazzan is saying the blessings for the congregation, it is as if we ourselves are saying the Amidah, which must be said standing. Based on this it is certainly correct to stand during the repetition of the Amidah. However, in many places this is not the custom. The Mishna Brurah points this out, noting (sadly) that "nowadays everyone does whatever they want - including sitting and chatting!" [It is certainly forbidden to talk during the Chazzan's repetition]. It would seem that if the local custom is to sit, one may join them so as not to "stand out". Also, in any case, if it is difficult for one to stand, one is allowed to sit (see Aishay Israel, 24, 20). May all our prayers be answered, Blessings.