Stage 1: Preliminary Design.
The first step before embarking on any major endeavor is always to plan out your actions. I personally find sketching out my ideas of paper and writing a list of requirements for my final product to be helpful.
Once the preliminary design constraints are established, find ways to make mechanisms work within them. For example, Each joint in the finger has some degree of lateral movement capability, but sufficient motion for virtually all tasks can be retained without this. As this would add an extra servo for each finger, simply designing the joints to converge on a single point in the palm saves greatly on weight and power.
Stage 2: CAD
Unsuprisingly, the next step after initial drafts and design concepts are down, the next major step is mocking up the first version of your prototype in a CAD program.