Strategic Mode is a single-player game mode where the player starts with with a small city-state (one shipyard-bearing City, with smaller towns around it) and aims to dominate the entire map.
Players have several options at the start. Most visibly, they can choose their coat of arms which will give their empire a bonus on the basis of its heraldic charge. Additionally, players may determine the details of the map (proportions of water/land & map size) and pick a difficulty setting (higher difficulties affect whether the player is issued a starting Ship, reduce/eliminate starting money & shrink the player's starting shipyard, along with improving AI performance). Finally, players may decide whether to opt into/out of the command-delay system (on by default; imposes a cooldown on issuing commands to particular ships based on the amount of bridges/cockpits present & staffed on the ship).
Once the map generates, the player can review their cities' defenses (click the city/town and use the Defences button), set the next technology target & funding level via the Research button, and review the empire's finances & secret-policing via the empire-stats button. Should the player have a starting ship, it'll be reflected next to the capital city with an airship or landship icon: clicking that will open a fleet-review pane where the player can review the ship.
The only way to increase income is to either conquer more towns & cities, or to eliminate various harmful Monsters (or other such encounters, such as Brigands or Pirates) that ravage the countryside and therefore reduce your territory's income. The player's imperial funds pay for Ship construction & maintenance, Research, any Spies the player sees fit to send (as well as any mischevious actions the player might then direct a Spy to perform) as well as the imperial Secret Police, the only defense against foreign troublemakers.
Espionage ("The Great Game")
Deploying a Spy allows the player to see the exterior of any defenses present at the Spy's location, in similar fashion to the Defences button for player-controlled cities. If a fleet is present, it will be similarly visible. Any construction (buildings or ships-in-progress) will be displayed as the blueprint shown when the player is building something; thus, the player can see "inside" whatever's being built. Spies will also give the option to bribe enemy ships, burn down enemy defensive buildings, or incite the town/city to revolt and break away from its current empire. If the player opted for the Guillotine arms at empire-creation, the city will join the player's empire; otherwise, it declares independence. If a Guillotine empire is present on the map but computer-controlled, it does NOT appear to inherit cities that revolt.
A given empire's Secret Police try to stop Spies from bribing, burning, or inciting trouble in their cities. However, it's unclear how the various levels of Secret Police affect foreign agents' ability to make trouble (drives up the cost? increases failure chance? informs when a Spy is present?) as compared to their cost, so in practice, a solid fleet and multiple defensive structures (in any city with a Medium or larger shipyard) are a better value for the money.
Airships work best in groups; generally, the small cannon-barges (more than one: they don't have much ammunition or coal and won't last more than a minute or two in battle) or the HMS Mutilatrix grenade-ship can be sensible options for the early going. The best advice is to be aggressive: the AI empires will grow & expand rapidly, and the player's empire will need to do so as well. It's best to attack first, win the fight if possible without losing a ship, and if it looks like a ship might get destroyed, withdraw the fleet, repair, and reinforce. (Then try again.)
Landships, once they become an option, can provide valuable support fire but greatly reduce fleet mobility, being restricted to roads and movement to the next stop-point, no further. In practice, players should build & deploy landships with a specific purpose in mind, and ideally construct them close to the intended use point.
Once players defeat an enemy territory, they have the option on how best to assimilate it (unless a Crown arms, or the territory started the map under the player's control; in these cases, it's immediately assimilated). Gently assimilating the territory takes a little while but doesn't damage its earning power; Brutally assimilating it does damage but speeds up the process, and Pillaging the territory greatly increases income while the takeover proceeds, but greiviously damages the territory once completed. Territories will recover given time.
The aim of a Conquest game is to control every City/shipyard on the map, thereby being the sole State power able to construct ships. Smaller towns contribute income and are therefore useful, but not needed for victory. Likewise, Monsters and other encounters present on the map can make life difficult, but do not block victory.
Upon conquering the final city, the player's arms are immediately displayed in a golden crown & wings frame, and the only option available is to accept ejection from that map. There is no post-conquest cleanup or pacification required or permitted; likewise, no ending plot, denouement, or final-stats screen.
In practice, smaller towns generally aren't worth defending: the maintenance on worthwhile defences is close to the amount a town produces. One should aim to keep one's shipyards safe, with priority to Medium and larger yards (Small & Tiny shipyards can't even repair most ships at a reasonable rate, let alone build them). Landship users may need to focus more on smaller towns to establish road control; airship users can strike enemy Cities first, thus reducing the threat of enemy fleets, and then mop up the surrounding towns at leisure. There are no "supply lines" or other logistical requirements to maintain fleets or territory.
It's really not cost-effective to maintain a Secret Police against the possibility of foreign troublemakers; just rebuild the defence or send a fleet to take back the territory. (This is another reason not to build defences: towns that revolt can be safely wrangled back.)
Brigands/Pirates & some Monsters like to raid cities. Unfortunately, they have a magic bypass-Pillage that lets them pillage territories just by being present in the battle screen for 2-3 minutes, rather than being forced to defeat the defenses & then pillage. As such, unless the defences can destroy any intruder within 60 seconds, it's best to either not defend or to just wave the raid through. (Even if the defences destroy all attacking ships/monsters, if they took too long to do so, the territory still takes the -60% income hit.) If a nearby fleet is fast enough to intercept the raiders en route to their target, feel free to do so, but don't send the fleet to defend territory directly. The Raid will still get through.
Once city-states start becoming larger than others, smaller AI city-states will Ally with each other to remain competitive. The player does not as yet have the ability to ally with anyone; rather, alliances are for now a way for the AI to quickly match the player-empire's size.