One leg of a ladder will rest on one step in a stairwell, but support needs to be added for the other leg to make a stable and safe platform. Some commercial ladders use an extendable leg. I made a sturdy and safe support from plywood.

Step 1: The Finished Support

The photo shows my finished support. It spans three stair steps because that corresponds to the width of the ladder's base.

Materials

3/4 inch plywood
Drywall screws (1 1/2 inch)
Wood glue

Tools

Table saw
Square
Tape measure
Drill
Screwdriver

Step 2: Measure the Stairs

Stairs have a tread (first photo) and a rise (second photo). There is a standard range for both, but they do vary to fit the space available without any partial steps. Here the tread is 10 inches and the rise is 7 1/4inches. (The tread is measured from the nose of one step to a point directly above the nose of the next.)

Step 3: Cut the Sides

I wanted to save plywood. I laid out the cuts as shown on the drawing, as if the side pieces were tucked around each other.
I moved the fence on my table saw to cut on the middle horizontal linke. This required holding the edge of the plywood against the saw fence while lowering the plywood onto the blade. Or, use a circular saw to make a plunge cut. Then I made crosscuts to saw on the vertical lines.
The horizontal line to be cut is the length of the stair tread. The vertical lines to be cut are equal to the rise of the stair steps.

Step 4: Cut the Top

The top piece needs to span the width of the ladder. Our ladder is 24 inches wide. I decided to allow some extra and made the top 29 inches long. I decided 10 inches of width would provide all of the stability needed. The support is very stable in use. I position the ladder feet toward the wall side of the support for extra stability.

Step 5: Assembly

Spread glue on the top edge of a side. Position it and pre-drill for drywall screws. Drive the screws home. Cut a piece to fit between the two sides. Glue and screw it to the first side and the top. Glue and screw the other side. Wait for glue to dry before using.
I set the piece between the two sides in so it would be under the leg of the ladder.

Step 6: In Use

This support supplies a stable footing for a ladder on a stairway. It is stable enough that one person can use it without the need for someone to hold the ladder. It does not solve all problems related to painting in a stairwell. You may still need to improvise ways to reach high places.