What is the best way of doing planks for abdominals training? How many should one do in one session of training? Should one try to hold the longest possible every time or a set time for as many repetitions possible?
You shouldn't try to hold a plank for the "longest time possible," but instead hold a plank for as you can maintain good form.
For instance, I end my abdominals workout with three planks (left-side, right-side, then standard). Normally I do planks for two minutes, but because the exercises are at the end of my workout when I am fatigued, I reduce the duration of each plank to one minute. If I were to go any longer, I probably wouldn't be able to maintain good form.
All of that being said, I don't believe there is any "magic number" of repetitions for planks. The amount of reps you'll want to do depend on what the intensity level of your workout is. In my example earlier I do three minutes of planks because I do a pretty intense ab/core workout, however it is perfectly fine for someone to only do 30-45 seconds worth of planks.