We say the Parshas Hatomid. Some say “Abaya havva messadder…” and “Ribon kol ha’olamim…” It is a mitzva to learn the explanation of “Abaya…” as well as the Parshas Haketores that we are saying daily – so that it can be considered in place of the actual offering. (Rama – MB1)
At least the Parshas haTomid should be said while standing like the actual offering was. (MB1)
The conduct of medakdekim is to sway while reading Torah – even Torah she’baal peh. Also to sway during birkas krias shema and Pesukay D’zimrah. (Rama – MB5)
During Shemoneh Esray do whatever will help your concentration – sway or stand still. Just don’t stand still while turning your head left and right – that is an arrogant way. (MB5)
On Shabbos and Rosh Chodesh add the verses of mussaf to the recital of Parsha haTomid. (ShA – Rama1)