The most common problem when upholstering corners -- on a dining room chair seat pad, for example -- is that wrinkles form. The reason is that flat upholstery fabric is being wrapped around a three-dimensional corner. You will not be able to get the deep creases out of some corners, no matter what you do. However, there are strategies that will give you the best possible corners.
Spread the fabric right side down on a work surface. Place the padded side of the seat board down onto the fabric, and wrap a 5 cm (2 inch) overlap of fabric over the back of the board on all four sides.
Secure the upholstery fabric in the centre of each side by stapling in the centre of the 5 cm (2 inch) strip of fabric overlapping the back of the seat. The fabric has to be secure on all four sides before you upholster a corner. You will not be able to upholster around the corner if the fabric slides out of position.
Imagine there is a line coming straight out of the corner you are going to upholster. It will be at a 45-degree angle to the flat edge of the board. Grasp the fabric right at the tip of the imaginary line. Pull it snug as you wrap it around the corner of the board. Staple in the centre of the fabric piece. Pull, using a firm grip, to get it tight enough to smooth out.
Place a second staple through the fabric about 1.2 cm (1/2 inch) from the edge of the board to hold the fabric down so you can make the next fold. Do this on both sides of the first staple.
Place the palm of your hand on the padded front side of the corner. Press firmly and smooth the fabric by sliding your hand around the board. Insert another staple in the fabric overlapping the back edge of the board. Repeat this on the other side of the corner.
Finish the three other corners in the same manner, starting with a staple at the imaginary line on a 45-degree angle.