1. **Plan and Measure:**
- Measure and mark the location of the corner wall.
- Plan the dimensions and height of the wall.

2. **Gather Materials:**
- Purchase lumber for framing (2x4 or 2x6).
- Acquire drywall sheets, screws, insulation, joint compound, and other necessary tools.

3. **Mark the Layout:**
- Use a chalk line or pencil to mark the layout on the floor and ceiling where the wall will be.

4. **Cut and Assemble Studs:**
- Cut vertical studs to the desired height.
- Cut horizontal studs to fit between the vertical ones.
- Assemble the frame on the floor, ensuring it's square.

5. **Install Corner Studs:**
- Place additional studs at the corner, creating a stable framework.

6. **Attach Frame to Floor and Ceiling:**
- Secure the frame to the floor and ceiling using framing nails or screws.

7. **Add Insulation:**
- Place insulation between the studs for energy efficiency.

8. **Attach Drywall:**
- Attach drywall sheets to the frame using drywall screws.
- Stagger the seams for stability.

9. **Tape and Mud Joints:**
- Apply joint tape over the seams.
- Use joint compound to fill gaps and smooth the surface.

10. **Sand and Finish:**
- Sand the joints once the compound is dry.
- Apply additional layers of compound as needed, sanding between coats.

11. **Prime and Paint:**
- Prime the wall to prepare for painting.
- Paint the wall with your chosen color.

12. **Clean Up:**
- Clean up the work area and dispose of construction debris responsibly.

Always adhere to local building codes, and if uncertain, consult with a professional or local authorities before starting the project.