In the context of the Craft, “Shadow work” is generally considered any meditation/ritual/magic that forces us to confront the darker, hidden parts of ourselves.
But originally, “Shadow work” was a phrase used by Carl Jung to describe the traits about ourselves that we have pushed away as negative and unwanted.
This could be traits that you see as evil and bad, to traits at are annoying, shameful, or pathetic.
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A quick exercise: When you see someone do something that annoys you or makes you angry, take a step back and ask yourself why. Then, look for a positive aspect to the negative quality you see in them, and make it a point to embrace and appreciate that. Journal! 
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But the shadow doesn’t have to be only unpleasant parts of your personality. It could be that which has been hidden, not allowed expression, pushed below the surface. Your shadow might contain positive qualities that you’re not owning, in addition to negative ones you’re not acknowledging.
Journaling is a good idea! Use this page and ritual to get you started:
Here are some other exercises that could help you too:
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Make art (any kind!) and then interpret it. Your art becomes a map of yourself. Especially in the long run.
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Sit for long amounts of time in contemplation or meditation. You can find guided meditations for shadow work as well.
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Make music, especially drumming or “singing out the demons”.
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Keep a dream journal. Exploring your dreams is a great way to discover what you may not be aware of consciously. There’s a course here on Spells8 to start your Book of Mirrors: the Witches’ Development Journal
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Tarot journaling. Go through your tarot deck and sort the cards based on ones you think are positive or negative and examine why. Find a card that reminds you of the behavior you want to change. Journal about the card’s symbolism. 🃠
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Perform healing rituals. Get therapy, especially from a Jungian or someone who understands your spirituality.
Shadow work is never “finished!”
I recommend you to work with the energy of the New Moon, also known as Dark Moon 
. There’s one coming soon!
Follow the exercises in this course: Shadow Work: Embracing Your Inner Darkness 
Recommended book: Sisters Of The Dark Moon: 13 Rituals of the Dark Goddess