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The field is divided into lanes. During each turn, each Pokémon can move into an adjacent lane, attack, or use an item; they can only do ONE of these things, and once they had taken their turn, they're turned sideways. Some moves can only hit an opponent in the same lane; others can hit adjacent lanes, etc. As long as a Pokémon is in a lane and is not dead, it will take any damage from Pokémon that attack that lane unto itself. To attack an opponent directly, the lane in front of you must be clear.
Pokémon cards are similar to Pokémon from the current TCG. They have HP and typing, with resistances and weaknesses to other types. One difference is that all game types are represented in the TCG. Pokémon typically have moves and may have abilities. Instead of energy, Pokémon take Supplies from the Supply Cache when they are placed down; they would have a certain cost, for example "2 spicy 1 any". Most moves consume a Supply card; the card is then returned to the Supply Cache. If a Pokémon is out of Supplies, it is unable to use moves, move, or use items. There are certain item cards that provide extra Supples when attached to Pokémon, but these extra Supplies do not return to the Supply Cache. Note that a Pokémon need only be in a lane to take attacks; it can take an attack regardless of whether or not it has already acted that turn.
Expeditioner cards also have HP, but they do not have moves, per se. Instead, they have various abilities that greatly affect the field. Instead of using Supplies for these abilities, they have Bond tokens, which represent their friendship and trust in you, the Expedition Leader. By doing things to increase their Bond to you and then cashing in those for abilities, they can turn the tide of battle. They take Supply cards to call into battle, but return the Supplies to the Cache once they are knocked out or reach zero Bond. They're comparable to planeswalker cards from MtG, but are more directly involved.