the establishment is essentially synonymous with "the system" of power and control, which is either in a national or international context
the actors behind an establishment are those that keep their current order in position,usually for their own benefit
this would include the government, civil service and chief bureaucrats, parliament, wealthy lobbies and large media and broadcast corporations. sometimes, one actor of the establishment will act as a mouth piece for other actors of it - and this can happen with numerous sets of actors at once - the media can be a mouthpiece for wealthy lobbies while the civil service can be a mouth piece for the government - that's the nature of human self-interest - our abilities to co-operate, even if would be in our ultimate advantage to do so, is limited by absences of trust, and self-prioritisation.
the actors of the establishment don't necessarily have to act together for one purpose and plan - they can conflict internally
the actors against the establishment don't fight politically as they are shut out - they act through media appeal, internet activity, unrest, mere discussions and debates between individuals, etc. and again, they don't necessarily all act as one whole, as there are different interpretations of what exactly is the "establishment", especially when it comes to questions of economic ideologies, feminism, "black lives matter", etc.
usually the only way to undermine an establishment is through an undermining of law(s) (often through evasion of apprehension), threatening the authority and abilities of the establishment, or merely slow and gradual change, especially in a (pseudo) democracy. right now we are witnessing the very slow pace of democratic enpowerment, as issues that are important to democracy are always brushed off by the parliament and government, and the media and wealthy lobbies, whom benefit from undemocratic institutionality, also brush off democratic-based issues in the system (when they cannot resist democracy, they often still control much of their audiences' political views simply via a hyperdermic needle effect) - hence we haven't fully debated full lords reform, PR electoral reform (not AV), the right of recall, etc. it's all clear if you consider how the establishment is set up and operates right in front of you.