The aid for trot is given with the outside leg (right leg) at the time of the right hind toe-down (begins stance phase for that leg). Hands have the function only to complete the connection through the horse so the aid can be answered in balance.
Preparation for the transition can be a half-halt. Half-halts can be strong or subtle but should be a clear, tactful request for the horse to understand rebalancing or adjusting for "what comes next." I prefer a half-halt with a combined stretch of upper body (avoids driving with the seat and "extra noise" from rein to bit) combined with a soft, definite touch of the calf that will ask for the transition itself. Thus there is a "library" of half-halts that go with dressage movements. Some riders will include a positioning of the poll or hindquarters with the half-halt. I prefer to separate the two and adjust the horse's spine prior to the half-halt. Whatever the choices, horse and rider should practice together until there is confident understanding of this communication by touch.
I am riding bareback in order that a saddle and pad do not hide the horse's shoulder and back muscles. Allow time for this movie to load (6.5 MB).
By stepping through the movie, you can observe a frame by frame understanding of the transition, which occurs slightly past its mid-point. Max makes this transition on the RH-LF diagonal pair in response to the outside calf aid. It is possible to ask for the transition on either diagonal by being clear about aids. This ability to distinguish diagonals is handy when asking for rein-back. If you make your own digital video movies, you can observe your own horse's response to your aids.