How does an individual assert a sense of dominance or inferiority in one self?

In order to “know thyself”, you need to learn to be honest with yourself, and suspend all judgement. Next comes the mindful observation of your thoughts – that’s all you need.

Finally ask yourself why you insist on labeling yourself this or that, in the first place

(this one’s optional, in regard to your question; for me that would be the logical follow-up).

I doubt that ‘self’ is a fixed persona. Dominance and inferiority are attitudes that ‘self’ expresses usually appropriate to the immediate situation. I think that ‘self’ is a repertoire of personae. However, examining your feelings, thoughts, and actions, and identifying those that mostly serve oneself and those that mostly serve others will be revealing.

Why would you pick that particular person as your ideal model? Why do you need either/or? Why do you feel a need for black or white?
Nietzsche had a few insights but he was far from correct across the board. I feel he was more wrong then correct. Read some other philosophers before you settle on a labeling ideal, if you feel the need to pigeon-hole yourself in such a limiting fashion.

@Trillian Quite the antagonist for an unbiased individual, but thanks for participating?

I believe that everyone is apt to see themselves as what they consider to be positive. What is positive varies from person to person, for instance in the example that you gave, the intelligent and witty person considers intelligence and wit to be the best attributes to have, whereas the other person considers humor and sociability to be paramount. However, what we consider to be the best is usually based on what we are.

The person who considers intelligence to be important is probably more naturally intelligent than social, and the person who prefers humor is probably more naturally funny than the intelligent person he criticizes.

A naturally dominant person would probably consider the master morality to be better, a naturally social-oriented person might consider it to be almost amoral, the slave-mentality being more kind to their motivations.

All in all, most people don’t consider themselves to be inferior. They adapt their mentality to consider whatever they naturally are to be superior. Objectivity is very hard to come by when judging anything. To the person with the master morality, the herd mentality seems trite and overly kind to the undeserving, and to one with the slave morality, the master morality seems Machiavellian and cruelly unappreciative of effort.