Wear

Sunblock
Bug spray
Long sleeve shirt
Hat
Sunglasses
Mask

Wear black bloc if appropriate. Black clothes, black headwear, black shoes, black bags. Hide your face, hair, skin, and tattoos. If your clothes or bags have any labels, cover them with black tape. The goal is to make everyone look similar and hide any contours that could identify you or anyone else.

Carry

No weapons - No guns, no baseball bats, no pepper spray, etc.
Bottles of water and snack bars, unopened, for yourself and others
First aid kit - Read the back so you know what's in it. Hardware stores sell these.
Signs
USB power bank in case a phone needs charging
"Dumb" digital watch and camera (optional) - These are easier to secure than a cell phone, and a watch is about $10. An old phone that's been factory-reset is also good.

The day before

Charge phones fully
Download offline maps using Organic Maps. Have everyone mark key points (Where we'll park, where the protest is, where we meet up in case of emergency) on their phones in case anything goes wrong.
Know your emergency contact. Pick someone who isn't attending the protest, in case your group is arrested.
Write checklists, timelines, maps, and phone numbers on paper and put them in your bags or pockets. If possible, put phone numbers inside your phone's case or on a sticker on the phone.
Have a lawyer and know your rights. See Lawyer, Passport, Locksmith, Gun

Before leaving

Tell your emergency contact what time you'll check in with them and what to do if you miss the check-in.
Set phones to airplane mode. Even if a phone's location feature is off, the cell radio, Wi-Fi radio, and Bluetooth radios will still emit signals that give out your location.
Consider disabling location tracking features such as "Find My iPhone", which may emit radio signals even when your phone appears to be off.
Take photos of everyone in your group. If you get separated, you can use the photo to ask people if they've seen them.
Write the phone numbers of your lawyer and your emergency contact on your arm using a marker. Make sure your clothes cover the numbers.
Turn your phones completely off. This should disable most radios (Except "Find My" on iPhones) and puts the phone into the "Before First Unlock" state which resists certain forensic tools that police will use if they take your phone.
Agree on a time and place to meet if anyone gets separated, even if it's just "Back at the car"

At the protest

Stay together. Even if you're safe, getting lost in a crowd is not fun.
Don't take photos of people. If you do, black out their faces, screenshot the photos to eliminate EXIF metadata, and try not to publish them. Know that people will take photos and video of you anyway.
Keep your phone locked. Some phones can take photos and video without a password.
Do not talk to news reporters. If they ask you something, point them to an organizer.
Do not talk to counter-protesters. You are not here to convince them. Your safety is more important. Do not make any gestures. If you feel compelled to say something, look away and walk away.
Do obey the law. Don't give yourself a reason to be in trouble.
Know that filming police from a reasonable distance is legal in some states.

If you are arrested

Find out where you are, location and building name. The police will not tell you once you're on the phone with someone.
Do not unlock your phone, do not give out your PIN. Use the phone numbers you wrote on paper or on your arm and ask to make a call.
You may have to repeat yourself dozens of times for hours - "I am invoking my right to remain silent. I need to talk to my lawyer. I am invoking my right to remain silent."
If you call someone, know that it will be recorded. Tell your lawyer or emergency contact where you are and figure out how to get out. Do not talk about anything that did or did not happen at the protest. [1]

Sources

Lawyer. Passport. Locksmith. Gun