Wear nondescript, solid color, layered clothing, making sure to cover any identifying traits (tattoos, birth marks, scars, etc.);
Goggles and a face mask are recommended: goggles for avoiding pepper spray, masks for tear gas (and Covid, stay safe folks!);
Write down your emergency contacts somewhere EMT's or other protesters can easily find (on the inside of your arm, for example);
Heat resistant gloves (can prove useful in many situations, plus they hide fingerprints);
If you have long hair, tie it up
Do bring:
Water, for hydration, treating tear gas burns and cleaning wounds in a pinch, bring extra if you can to account for others that might need it;
Snacks: sugar packets, cereal bars, some fruit, etc;
Some pocket money for emergencies as well as your ID;
First aid-kit: rubbing alcohol, band aids, gauze can all be useful in a sticky situation;
Ear plugs;
Don't bring:
Your cellphone, if you absolutely must have a phone, use a burner, the more analog the better;
Jewelry: necklaces, rings and earrings/piercings can get caught in a million different places and you could get hurt;
Anything incriminating: no illegal substances/weapons/other that might give cops a reason to put you in custody;
Contact lenses, not only can they fall off, if hit by tear gas it will just make it burn for longer, and taking them out proves even harder, take glasses instead.
How to get involved:
Seek out local organizations that might be organizing protests in your area;
If possible get at least one friend to go with you, ideally a bigger group so you can keep each other safe
Make sure to check the organizations beforehand! Some orgs may be working with law enforcement to keep tabs on protesters, exert caution when researching.
General Advice
Stay away from choke points: narrow alleyways, stairways, and similar tight or overcrowded places;
Don't talk to cops, ever. If you are detained, immediately ask for a lawyer and say nothing else. Only talk to your lawyer, if they allow you to make a phonecall, avoid telling any relevant information to your family/friends. Cops can't legally listen to your call with a lawyer, but they will listen in if you call a family member;
Don't talk to the press or media. They will just twist your words to fulfill their agenda and give justification for further repression of protests.
If you must bring a phone (please don't), absolutely do not post on social media, especially live-posting-- you're just doing the cops' job for them;
Stay calm but vigilant, look out for anyone that might be out to cause trouble within the protesters, and be mindful of undercover cops. Caution is the key word here.
If you wanna record/photograph the protest, use a separate camera instead of your phone, but avoid bringing your biggest most expensive camera gear, it will just be something else to worry about. Blur out any identifiable faces before posting.
Stay safe, vigilant and united. Avoid direct confrontation with cops as much as possible, keep your distance as best you can, and if you smell trouble, back away in the safest possible way.
I would say bring physiological serum. Be careful of the legal advice, it is very country dependent.
And maybe be careful of bringing water in plastic bottle and not metal, it's heavier and in some countries they could argue that this is a weapon and arrest you for that