Here we will list and explain the general protocol the Borg observe during encounters and combat. Explanations will include why and what advantages and disadvantages each action presents.
Ship to Ship Combat Procedures
Scenario: Single Targets Borg vessel versus alien vessel
In the event of first contact with a vessel of unknown or greater threat potential Borg vessels may erect a dispersal field against unaware targets with their shields still, down making it invisible to standard sensor scans for threats as they approach at impulse speed. 
During this time the Borg vessel will make all appropriate preparations for a first contact encounter to achieve maximum combat effectiveness Whilst feigning itself to be as least threatening as possible such as; sending drones in to regeneration until necessary activation and keeping offensive and defensive systems unpowered. (Th)This time is used for constructing or preparing the appropriate weapons and defence modifications to aid in the capture of the vessel like shield training torpedos, warp field destabilizing weapons and laser cutting beams.(Th)
In the event of first contact with a vessel of unknown threat potential whose shields are down upon initial contact, the Borg vessel transports a single drone to the engineering section in order to download the vessels technical schematics and ship database. The vessels lifeforms are ignored at this stage until the threat level of their technology has been established. 
Scanning other Potential Threats
In order to enhance situational awareness of other potential threats, if the Borg ship is already assigned to engage / is already engaging a specific target species and comes across an unidentified vessel, one ship is dispatched to move in closer and perform a scan using the polaron beam. (VOY - "Scorpion")
Hails vessel When the vessels technology or lifeforms have been scanned and deemed worthy of assimilation the Borg vessel will then hail their target and inform them if their intentions, warning them to surrender and that resistance is futile. ("Star Trek First Contact", , "Best of Both Worlds", VOY - "Scorpion", "The Raven", "Drone", "One", "Dark Frontier", "Hope and Fear", "Endgame") In the scenario that the Borg vessel is a hybrid post-assimilation vessel, the Borg will hail their target and inform them that resistance is futile, however they will not identify themselves as Borg. ENT - "Regeneration"
Comment: it's entirely possible they do not identify themselves as Borg due to having no link to the Collective, In Regeneration they had a local consciousness consisting of the drones aboard Enterprise and those aboard the Arctic Transport.
Engages Tractor-Pulse and holds the vessel - preventing it from escaping or performing combat maneuvers while the Borg vessel begins wearing down the defences of the target vessel. ("Star Trek First Contact, , Best of Both Worlds, VOY - Scorpion, One, Dark Frontier, Hope and Fear, Endgame")
Should the tractor pulse be disabled or uneffective, engines are targeted second. Should the target attempt to flee, the Borg vessel pursues their target and continues to wear down their defences with weapons fire (VOY -"Endgame") and disrupt their engines using (who torpedoes ?)
Cutting beam In first contact encounters, when the vessel possesses an unknown hull alloy composition the Borg vessel will use the cutting beam to extract a non-vital section from the ship for analysis. (TNG - Q Who, Best of Both Worlds". In the scenario that the Borg vessel is a hybrid post-assimilation vessel, the cutting beam will be deployed to acquire additional alloys which will be enhanced with Borg armour modifications and used to increase both then mass and to bolster the defences of the assimilated ship. (ENT - "Regeneration").
- Targeting - the Borg opt for a direct, simplistic and efficient attack pattern: targeting one system at a time for efficiency, they do not scatter their fire. Typically targetting shields first, followed by engines (VOY - "Collective, Unimatrix Zero"). The Borg do not typically target the weapon systems of other vessels as they purposefully prepare for incoming fire, allowing themselves time to adapt to the targets weapons. (VOY - "Collective")
Comment: Targets Frontal shields Unimatrix Zero if Cube is struggling to adapt to the weapons fire?
- adapting purposefully taking fire to adapt
Exploiting Opportunities - such as tapping into transporter beams to beam drones on-board the vessel. (VOY - "Dark Frontier")
- exchanging fire - inverted phaser beam with feedback pulse "one"
- Once shields are down, transports drones
Boarding Tactics Overt
Scenario: Full drone compliment, Borg ship intact and engaging.
- Drones often beam aboard the bridge amidst a confrontation in an attempt to seize immediate control of the vessel. (VOY - Dark Frontier, Star Trek First Contact) Assimilating the commanding body of the vessel allows the collective to: severely disrupt all organised on-board ship functions and resistance from host species. Gain full computer access, allowing the collective to disrupt all on-board communications and seize control of the vessel remotely VOY - "Scorpion".
- Should the attempt to seize the bridge be unsuccessful or not possible drones will be dispatched throughout the ship to install a device which, upon receiving an activation signal will disrupt the warp plasma networks. Disabling main power to the ship whilst the device remain active. ENT - Regeneration
- Damaged drones are beamed back onboard the Borg vessel to be repaired or for the purpose of salvaging their components. In the event another drone is nearby he will salvage several components by hand and (th)immediately intergrate them in to himself or another drone upon returning to the Borg vessel(th).
Boarding Tactics Covert
Scenario: minimal drones, undetected, loss/retreat of Borg ship, isolated.
If the host ship is expected to encounter a Borg vessel before the drones can be defeated, the drones will be dispatched throughout the ship to install a device which, upon receiving an activation signal will disrupt the warp plasma networks. Disabling main power to the ship whilst the device remains active. ENT - Regeneration
If no further Borg vessels are expected to assist then the drones firstly proceed very cautiously, deactivating the vessels intruder alert and then proceeding towards the vessels Engineering section via conduits and hidden junctions. Assimilating unsuspecting crew members encountered along the way and using ambush tactics until finally they attack engineering (if Queen is present, establish a central plexus for her safety), blocking communications and disabling the internal com system within engineering before they proceed using their standard direct approach.
In the event the vessel is a great distance from Borg space such as within an entirely different quadrant the Borg perform the following:
- The drones will pause their advances and assimilate the vessels deflector control.
- Drones will construct an external beacon which when completed is capable of sending a message to the Collective which also provide the vessels co-ordinates.
Following which the Borg drones continue assimilating the lower decks first, working their way towards the bridge for the vessels total assimilation.
Anti boarding party procedure - how do the young react when boarded ?
- Damaged drones are left behind and ignored for maximum efficiency until the objectives have been accomplished. (ST:First Contact)
Scenario: Single Borg Vessel Vs. Multiple Enemy
when engaging multiple ships no one ship is targeted exclusively, all engaging ships are retaliated upon and attacked according to the standard attack sequence is performed, respecting the subsystem targeting priorities on a ship by ship basis. Logic behind this is there are no ships left unscathed in any engagement and each attack against the ship is retaliated upon .