The term of “looking within” is not, of course, used literarily. It is not about seeing your internal organs but, rather, seeing yourself beyond the sphere of societal interactions, beyond the sphere of day-to-day regularity; seeing yourself as a distinct individual with some degree of bigger depth; depth that is otherwise overlooked.
There can be many ways where you can discover the deeper aspects of yourself, and many of them are being done through voluntary isolation, AKA, from solitude. That is because when you are alone there are less things and beings to distract you from whatever you’re doing, hence the importance of being alone and the relative silence of solitude for concentration.
The said aspects of yourself are, technically, always present within you regardless of the situation. It is just that we don’t regularly pay enough attention to them, due to the necessity of focusing on other things for our survival and development.
Ask someone random what are they’re thinking about, and it’s likely that they won’t know what to answer, even though we as humans are always producing and experiencing thoughts. That is the irony of these aspects of ourselves — we “breathe” them in almost if not all of our moments, but without enough awareness, we won’t be able to describe them and what they entail.
Dedicate some time to listen to your thoughts, and even record them in whatever form, as your thoughts are the gates to the desired aspects of the self you may be looking for.
You can thus know that you have looked within yourself in a sufficient matter when you are able to properly describe what you’re thinking about when asked so in whatever situation. You can see it as a test of the current capacity of your self-knowledge. Have someone to ask you this exact question from time to time, and you may be able to pass this test the more you practice the focusing and/or recording of your thoughts and feelings, just like any other test that requires an immediate answer.