The short answer to your question is that you must declare your method signature for the slot to connect to, using the slots method:
class MainGUI < Qt::MainWindow
  # Declare all the custom slots that we will connect to
  # Can also use Symbol for slots with no params, e.g. :open and :save
  slots 'open()', 'save()',
        'tree_selected(const QModelIndex &,const QModelIndex &)'
  def initialize(parent=nil)
    super
    @ui = Ui_MainWin.new # Created by rbuic4 compiling a Qt Designer .ui file
    @ui.setupUi(self)    # Create the interface elements from Qt Designer
    connect_menus!
    populate_tree!
  end
  def connect_menus!
    # Fully explicit connection
    connect @ui.actionOpen, SIGNAL('triggered()'), self, SLOT('open()')
    # You can omit the third parameter if it is self
    connect @ui.actionSave, SIGNAL('triggered()'), SLOT('save()')
    # close() is provided by Qt::MainWindow, so we did not need to declare it
    connect @ui.actionQuit,   SIGNAL('triggered()'), SLOT('close()')       
  end
  # Add items to my QTreeView, notify me when the selection changes
  def populate_tree!
    tree = @ui.mytree
    tree.model = MyModel.new(self) # Inherits from Qt::AbstractItemModel
    connect(
      tree.selectionModel,
      SIGNAL('currentChanged(const QModelIndex &, const QModelIndex &)'),
      SLOT('tree_selected(const QModelIndex &,const QModelIndex &)')
    )
  end
  def tree_selected( current_index, previous_index )
    # …handle the selection change…
  end
  def open
    # …handle file open…
  end
  def save
    # …handle file save…
  end
end
Note that the signatures passed to SIGNAL and SLOT do not include any variable names.
Also, as you concluded in your comment, it is simpler (and more Ruby-esque) to do away with the "slot" concept altogether and just use a Ruby block to connect the signal to invoke whatever method you like (or put the logic inline). Using the following syntax, you do not need to use the slots method to pre-declare your method or handling code.
changed = SIGNAL('currentChanged(const QModelIndex &, const QModelIndex &)')
# Call my method directly
@ui.mytree.selectionMode.connect( changed, &method(:tree_selected) )
# Alternatively, just put the logic in the same spot as the connection
@ui.mytree.selectionMode.connect( changed ) do |current_index, previous_index|
  # …handle the change here…
end