What are my Rights if I want to Protest?

Generally, the first Amendment provides a lot of protection for expression:
“Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.”

So how does this apply to Protests?

First, its critical to point out the significant distinction between a “protest” or “demonstration” and “Riot” or “Looting”. It may seem to obvious to even clarify, but the events in the last few weeks have caused some confusion. Protests and demonstrations are gatherings to express ideas or communicate a position, usually concerning politics, policy or government. They are peaceful expressions of ideas, usually en masse to show there are factions of society that feel under-represented politically. Marches, speeches, handheld signs and gatherings are clearly protected by the First Amendment's prohibition of the government stopping peaceful assembly.

When can a Protest become Illegal?

Any gathering that may impede public access to common areas may be a violation of municipal or vehicle codes, and large gatherings may need a pre-issued permit. Generally speaking, gatherings in public areas should not require permits if access is not impeded and no vehicle or pedestrian codes are violated.
Can words alone justify an arrest?
Constitutional law on freedom of speech is replete with examples of speech that may seem obscene or profane, but the general rule is “Conduct, not Content”, in other words, its your actions, not your words, that can get you in trouble. However, there are some situations where words in particular situations can be illegal, such as contemplated in Penal Code Section 415:
Any of the following persons shall be punished by imprisonment in the county jail for a period of not more than 90 days, a fine of not more than four hundred dollars ($400), or both such imprisonment and fine:
(1) Any person who unlawfully fights in a public place or challenges another person in a public place to fight.
(2) Any person who maliciously and willfully disturbs another person by loud and unreasonable noise.
(3) Any person who uses offensive words in a public place which are inherently likely to provoke an immediate violent reaction.
Taken in the context of a demonstration, a person could be arrested for a violation of 415(3) PC if an officer believed a person was intentionally trying to provoke someone into an “immediate violent reaction”, which is as close to content-based speech restrictions as the law will allow, and tip-toes the line between a peace-keeping function violation of freedom of speech.

What about Delaying/Resisting/Obstructing an Officer?

The full text of the statute:
148 (a) (1) Every person who willfully resists, delays, or obstructs any public officer, peace officer, or an emergency medical technician, as defined in Division 2.5 (commencing with Section 1797) of the Health and Safety Code, in the discharge or attempt to discharge any duty of his or her office or employment, when no other punishment is prescribed, shall be punished by a fine not exceeding one thousand dollars ($1,000), or by imprisonment in a county jail not to exceed one year, or by both that fine and imprisonment.
Again, things get a bit gray in the context of a demonstration or rally, and focuses on conduct, not speech content. Obstructing/Delaying/resisting an officer requires only that you know the person is a cop, and that you intentionally fail to comply with his order.

What happens if a cop tells you to go home, but you are not breaking the law?

The Calcrim jury instruction provides an exception to the requirement to follow a cop's directions:
A peace officer is not lawfully performing his or her duties if he or she is (unlawfully arresting or detaining someone/ [or] using unreasonable or excessive force in his or her duties).  Therefore, it's a defense to a 148 charge to defy an officer if the arrest is unlawful or conducted with excessive force.

Can going limp and not helping a cop arrest me be a violation?

Unfortunately, the law addresses this concept as well:
If a person intentionally goes limp, requiring an officer to drag or carry the person in order to accomplish a lawful arrest, that person may have willfully (resisted[,]/ [or] obstructed[,]/ [or] delayed) the officer if all the other requirements are met.

What should I do if I am arrested during a Protest?

Call 760 643 4025 for help, your actions may be constitutionally protected or justified.