you can increase your desythesis chance by using items such as Bacon Broth and Tinker's Calm, and since one is a food and the other is a potion, you can stack their effects. Also in gear you're wanting to desynth, melding any kind of materia to it will increase the chance of successful desynth. As for how to proceed, you can follow the guide in the beginning but eventually you can just gauge your progress by looking for the desynth value that is now listed on all items you can break down and go from there compared to what you have built up.