Most of what you do in AppMockUp Studio has a key for it. Ctrl/Cmd means Ctrl on Windows and Linux and Cmd on a Mac; Alt is Option on a Mac.
Screenshots
Alt + S - Add a new Main Screenshot
1 to 0 - Select Main Screenshot 1 to 10
Ctrl/Cmd + click - Select an Instance Screenshot
Delete or Backspace - Remove the selected screenshot
Selection
Escape - Step out one level: from a sticky or highlight to its layer, from the layer to the screenshot, from the screenshot to nothing
Click an empty part of the stage - Deselect everything
Delete or Backspace - Remove what is selected. With a sticky or highlight selected, only that sticky or highlight is removed and its layer stays selected
Ctrl/Cmd + Shift + H - Hide or show what is selected: a layer, a sticky, a highlight or a device. On an Instance Screenshot it is hidden for that device only
Moving and Rotating
Arrow keys - Nudge the selected layer, sticky or highlight
Alt + arrow keys - Nudge in fine steps
Shift + arrow keys - Nudge in large steps
R + arrow keys - Rotate
While Dragging on the Canvas
Shift - Keep a move on one axis, snap rotation to 15° steps, lock the aspect ratio while resizing, step the corner radius in tens
Alt - Round a single corner instead of all four
Ctrl/Cmd - On an Instance Screenshot, save the change as an override for that device
Text
Double-click a title, subtitle or caption - Edit it on the canvas
Enter - New line
Escape or Ctrl/Cmd + Enter - Finish editing
Ctrl/Cmd + double-click - On an Instance Screenshot, create a text override for that device and edit it
All the details are in How to Edit Text on the Canvas.
Images
Double-click a device - Choose its screen capture
Double-click a background, icon or image with an image fill - Choose that image
Ctrl/Cmd + V - Paste an image from the clipboard onto the selected layer. With nothing selected, make a new screenshot from it
History
Ctrl/Cmd + Z - Undo. The history holds 100 steps
Number Fields and Sliders
↑ / ↓ - Increment / decrement by 1
Shift + ↑ / ↓ - Increment / decrement by 10
Double-click a slider knob - Reset to the default value
Highlight Crop Editor and Full Quality Previews
Alt + click - Select the region under the cursor (crop editor)
Shift + Alt + click - Add that region to the crop (crop editor)
Shift while resizing - Keep the aspect ratio
Alt while resizing - Resize around the center
Space + drag, or the middle mouse button - Pan
Ctrl/Cmd + scroll, or pinch - Zoom