Recognize that racism and anti-Blackness are the water we swim in, they are so constant as to be invisible. Media literacy is important, and we're constantly bombarded with messages of racism and white supremacy.
The modern concept of "race" has been around since the 18th century, so it has become a deeply-embedded part of our culture.
Recognize that it will probably be a life-long journey to unlearn racism.
Accept that you are occasionally going to make mistakes and cause harm to others. Perfection is impossible.
When someone points out that you've caused harm, do not get defensive. Instead apologize, take responsibility, and resolve to do your homework and make changes to avoid repeating that mistake.
Other articles that list dos or don'ts of being an anti-racism ally:
"It’s not supposed to be about you. It’s not supposed to be about your feelings. It’s not supposed to be a way of glorifying yourself at the expense of the folks you claim to be an ally to. It’s not supposed to be a performance. It’s supposed to be a way of living your life that doesn’t reinforce the same oppressive behaviors you’re claiming to be against."