Caveat — I am white. Take my words with a HUGE grain of salt, and instead go listen to the POC who are linked below.
Don'ts
Don't be a white savior. Don't be paternalistic, and don't encourage dependence. Rather, offer assistance in a way that fosters autonomy and empowerment.
Don't be a typical white liberal, whose words suggest they're against racism, but whose actions don't differ much from white conservatives. See Malcolm X's criticisms of the white liberal and his descriptions of the wolf versus the fox[2][3].
Don't make your anti-racism efforts the center of attention. Listen to POC leaders, and point other white people towards POC content-creators and leaders.
Recognize that racism and anti-Blackness are the water we swim in, they are so constant as to be invisible. Media literacy[2][3] 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.
See also
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."