(If you haven't already, you should start by reading the Basic Card Game Rules)
There are five types of Planning Cards: Locations, Opponents, Allies, Scars, and Events.
Battles take place in a growing & changing cityscape - composed of whatever bits and pieces players have put into their combat decks. Mostly a city is made up of locations (like buildings) and opponents (like military vehicles).
The first city card played goes into the center of the play area. All subsequent city cards are played in a row, so that kaiju are “furthest” from the card played most recently. In order to move through the city, kaiju must play combat cards with Move values.
All active characters are adjacent to the current city card. During any battle, after resolving a round's damage, kaiju may use the Move value on their combat card to move through the city. For each point of movement:
Movement is always optional, not mandatory. You may use some of your movement, or all, or none.
City cards often have ongoing effects - Tanks try to damage kaiju, Office Complexes make the whole city tougher, Nuclear Power Plants generate energy, and so forth.
When an active character decides to Rampage, they are engaging the entire city in combat. The rampaging character fights the adjacent city card just as if it were a kaiju, and one opponent uses their combat hand & energy tokens to play on behalf of the city. (If nobody wants to play on behalf of the city, then the rampaging characters simply plays as many sword cards as they like, with no resistance to slow them down.)
This plays out just like a regular combat, with 3 important distinctions:
Certain attacks deal damage over a wide area - indicated by the RANGE value on the card. When The Sword plays a card with a RANGE value, they may deal 1 point of direct damage to a city card. Range:1 allows them to deal damage to the adjacent city card only. Range:2 allows them to deal damage to the adjacent card OR the card beyond it, and so on.
If collateral damage KOs a card, it is placed into your GLORY pile as normal.
A rampaging character may NOT deal collateral damage!
When a player is playing combat cards on behalf of a city card, those cards may NOT deal collateral damage.
In some situations, you might have a Team Fight - where multiple characters enter on one or both sides of the combat. These play out just like normal fights, with just a few differences:
Cards in the city can also be attacked and damaged for GLORY. The glory earned from defeating a location or opponent is the black number in a yellow box in the top-right corner of the card.
Kaiju cards do not have a GLORY number - they are always worth 5 GLORY (unless otherwise specified by rules text.)
Many event cards are worth GLORY - the rules on the card specify their value.
If you are asked to put random planning cards into your GLORY pile, put them face-down to prevent confusion. face-down cards are always worth 1 GLORY.
If you are told to “gain” GLORY with no specific card to represent it, use tokens.
When any player has 20 or more GLORY, the game ends immediately and that player wins. If multiple players reach 20+ GLORY at the same moment, the highest total wins. If there is a tie - the player with the most glory worth of characters still conscious wins. If that number is the same - the game is a tie!
If at any time only one player has characters left on their team, that player immediately wins the game, regardless of how much GLORY everyone has.