Mouse click or keyboard command
What it does
Click a measure
Selects the full measure
Click and drag diagonally across any measure region (partial or whole measures)
Selects the measure region
When you select a partial measure, Finale highlights an area from the left edge of the first selected note to the right edge of the space after the last selected note, to help reinforce the fact that you’re actually selecting a stretch of musical time.
SHIFT-click and drag diagonally across any part of a measure
Selects full measures only
SHIFT-click before or after a selected region
Extends the selection to wherever you click
Hold down SHIFT and press the left or right arrow keys
Expands or contracts the selected region in entry-by-entry increments
...measure-by-measure increments if the measures are empty. Specify you want to adjust the beginning or end of the selected region by pressing the left or right arrow key first respectively.
With the Selection tool 
selected, double-click any partial measure selection
Or, ALT-click any partial measure selection with any tool that permits regional selection
(The selection can include any number of measures starting and/or ending with a partial measure)
Expands the selection to include full measures.
With the Selection tool selected, double-click a full measure
Or ALT-click any full measure selection with any tool that permits regional selection
Expands selection to include the full stack.
Click to the left of the staff
Selects an entire staff
SHIFT-click to the left of a staff
Extends the selection from any other staves you've selected
From the Edit menu, choose Select All or press CTRL+A
Selects the entire document
Hold down CTRL+SHIFT and press the left or right arrow keys
Expand or contract the selected region by full measures
Hold down SHIFT and press the UP or DOWN ARROW keys
Expands or contract the selected region vertically (staff-by-staff)
Hold down the SHIFT key and press END, HOME, PAGE UP, and PAGE DOWN
Select all measures right, left, above, or below a selection
