Speaking on Irish Rail 071s, which have a high speed GM engine, there is a slight delay as the fuel racks run up, which can cause a problems when starting away on a rising gradient.
To overcome this the practice when stopping is to release the train brake, and hold the train on a light application of the loco straight air. The real masters can shuttle from one to the other as the train rolls to a stand with not even a jerk.
On getting the right away, the power controller is moved to position 1, the engine speed runs down slightly and then starts to run up as the fule racks run up into position, you then move the power controller to position 2 and as the loco takes the weight, you ease off the straight air. You can sense the correct time as the loco starts to lean forward just before she starts to drag the brakes. If you get the release wrong the loco will snatch the train but done properly you are bleeding off the straight air as the wheels are freed up to rotate.
Starting away on the level and a falling gradient is simply a question of opening the power controller up to position 1 then as the speed dips, opening it up to position 2 and then forward steadily to full power.
These clips illustrate.
http://www.youtube.com/watch?v=k5EVXqYDEWc&feature=related
http://www.youtube.com/watch?v=rIV4EobOvhA&feature=related
On this clip at 2:18 you can see him shuttle the train and stright air brakes, and at 2:40 you can hear the drop as the power controller is opened and at 2:59 you can hear as the Driver opens up into position 2, as the loco takes up the train.
http://www.youtube.com/watch?v=eROHKB2NjRM&feature=related
This is probably the best departure, with a straight transition through the power controller positions. You can imagine what it was like on the footplate when these beasts were opened up.