The main thing that makes ash_state_machine different in design from other state machine tools is that the actions are still the source of truth. The state transitions defined in the state machine block describe what transitions are allowed, and then in a given action you actually perform the state transition.

attributes do
  attribute :unspent_cents, :integer, allow_nil?: false, default: 0 
end

state_machine do
  transitions do
    initial_states [:waiting_for_coin]

    transition :coin_inserted, from: :waiting_for_coin, to: :drink_selection
    transition :drink_selected, from: :drink_selected, to: :drink_preparation
  end
end

actions do
  update :coin_inserted do
    argument :coin_amount, :integer, allow_nil?: false
    change atomic_update(:unspent_cents, expr(unsepent_cents + ^arg(:coin_amount))
    change transition_state(:drink_selection)
  end

  update :drink_selected do
    argument :selection, :atom, constraints: [one_of: [:coke, :diet_coke]]
    change set_attribute(:drink_selection, arg(:selection))
    change transition_state(:drink_preparation), where: [CanAffordDrinkSelection]
  end
end

This is just an example, certainly not 100% correct, but thrown together as an example of what it looks like in practice.