When to finish before assembly
Most of us apply linear thinking to project building: Cut parts to size, fasten them together, and then apply finish. But good woodworkers don't always finish last. In some cases, it makes sense to apply finish before you glue parts together.
For example, in the assembly shown above, the spindles will be less than 1" apart after being joined to the rails. Brushing on the stain (and later, the topcoat) before glue-up gives you easy access to all sides of the spindles, as well as the full edges of the rails, and avoids uneven coloring from stain stuck in confined places. Painter's tape keeps finish off the tenons, preserving a clean surface for glue-up.
Stain when access is easy
It often makes sense to finish partial assemblies, too. As shown below, staining the cabinet carcase before attaching the back or face frame allows you to work from both the front and rear to reach all surfaces. Staining with those pieces omitted also reduces shadows that mask areas of uneven coverage and eliminates corners where three surfaces meet. Stain, especially a gel type, collects in those hard-to-reach areas, creating a blotch.
Keep the contrast
Some projects may have parts with different shades of finish, or stained parts next to unstained parts. Staining before assembly ensures each piece gets only the proper color, below.
Prevent accidental reveals
It also pays to finish solid-wood pieces when expansion and contraction could reveal unfinished borders, such as with a raised panel in a frame-and-panel assembly, or the ship-lapped cabinet back shown below. With stain applied to the full width of their front faces, an unfinished edge will never show as the boards swell and shrink across their widths.