Measure and cut mesh to accommodate the opening in the fireplace screen. Make the mesh 2 inches larger on all sides than needed.
Lay the mesh on top of the screen frame. Unroll a length of spline. Lay it down along one edge of the mesh.
Press the wheel of a spline tool into the spline, forcing it into the channel or groove along the frame. Run the wheel along the entire side of the spline and mesh until it is secure in the frame. As it enters the channel, the mesh will become more taut.
Stretch the mesh taught across the frame, applying pressure and keeping the mesh tight. Lay down more spline and work the tool through the material, pushing it into the channel along that side of the frame. Use short strokes for best results. You should now have the two opposing sides secure.
Flatten the mesh across the left side of the fireplace screen. Fit it into the channels using the same method with the spline tool.
Attach the final side of mesh. Cut off any excess material from all sides of the fireplace screen.