The founding fathers saw political protest as a necessary component of a healthy civic life, that it should kick into gear whenever some political grievance should crop up, like some recurring organic homeostatic function, whereas today the protest appears much more as some delineated, contained game which is loathed and held in contempt by the authorities and their sycophants.
This is not to diminish the efforts of the protesters. They are doing good and necessary work. But it is always interesting to see how political dissidence actually works in real world conditions, especially in a conservative society such as this one.
The founders could probably be referred to as radicals in their day, though the extent of the radicalism and revolutionary tendencies of each founder could be debated, which I'm not going to get into. And what radicals typically envision is a society in which their radical inclinations are made a regular occurrence in the operation of an ideal society.
What usually seems to happen instead (or better, what seems to happen in cycles in this mature stage of civilization) is that moments of political radicalism, if they are to be transformative on a system-wide scale, come and go in different eras. There are periods in which the energy emanating from below bursts open the rusted jaws of convention, forcing change, and then there are periods in which convention prevails, buttressing its preferred shape of society against the transformational powers of political movements, or at least compromising with the movements in return for a watered-down radicalism.
Perhaps in a healthy society with a strong sense of collective security, protests could be encouraged and even communicated with. But in a sick society such as this one - which fears constant disintegration at every turn, and which resists any kind of meaningful change - protest becomes a sort of game due to the opposing and irreconcilable aims of its participants, as well as the constrictive bounds of what's left of civic life. Competitive games take their tension from the opposing aims of the competing players, and modern protests, with their intricate games of psychological warfare, are similar in structure, though the stakes are certainly higher.
So. The object of protesters is to force a dialogue that political elites refuse to entertain, and this has to be done by disrupting the elites' precious system. It requires a dramatic and vivid impact, and a forcing of the dysfunction of business as usual, to jolt a society into a mode of self-reflection. Walking down the streets and shouting with signs is not enough, though it can raise some awareness at least. If you can be ignored, business can continue, and usually that is all that is required for a protest movement to become ineffectual.
Protesters rely on social media, limited communication encryption, theatrical tactics, and various methods of direct disruption, such as blocking roadways, chaining themselves to important buildings or objects, sitting in, making noise, and directing public attention at offending individuals, institutions, classes, or other objects. Some protesters believe in property destruction and other destructive acts, though this observation is complicated by the fact that there were actual undercover cops in Berkeley smashing windows and instigating looting. It isn't always clear how these movements unfold.
The object of police on the other hand is to maintain the shape of society. Police seek to minimize the protesters' impact in several ways, such as by neutralizing the power of protests with various tactics. Police rely on containment and inter-agency coordination, and legal monopoly on the instruments of violence. Police will carefully coordinate individuals and material resources to find and isolate accumulations of human mass, and then direct them through parts of the city which are removed from important commercial activity, taking care to use intimidating tactics which cause gradual dispersion.
Dispersion is the primary police aim. There are reports of the police now using drones to confuse protesters as to the location and direction of the protests (we checked Twitter feeds and searched for circling helicopters to find ours). The drones pose as helicopter decoys, confusing protesters as to the location of the march, further preventing accumulation.
The accumulation of human mass mentioned above is perhaps the most important parameter. The protesters want a large, vibrant, growing mass, the size and spectacle of which communicates a public will. The mass also changes properties of the protest movement itself; it amplifies expression. With the presence of social witnesses, numerous protesters are more likely to vigorously express some point of view, or they are more likely to commit a certain pointed, political action. The mass movement creates the conditions for finer, more vigorous public expression, with types of public expression varying as more varying individuals become attracted to the protest. And then a greater body of people is simply more capable of disrupting commercial or civic centers.
The police want more than anything to direct, contain, and eventually disperse this mass, through force if necessary. They are less interested in lone individuals breaking off of the protest; as soon as you leave the crowd, you are typically free to walk away, unless the police are breaking off and isolating individuals to arrest out of spite.
This protest activity continues in cycles - especially after particularly egregious violations of justice - and then abates as the energy disperses, with the most dedicated activists and organizers moving on to other projects if there is no more possibility of effective action. Of course there are plenty of future opportunities for the outpouring of public sentiment. There is no shortage of pressure to be released as useless heavy things continue to press upon the body politic.