Step One:
First, we must determine how long to make our border strips. This is done by adding the length of the edge of the quilt top to the width of the border (twice) and giving yourself a bit of extra length to work with. I prefer to add six inches.
Let's say our quilt is a 50" square and we want to add a 4" mitered border.
  Our formula is 50 + 4 + 4 + 6 = 64

Step Two:
Pin the top and bottom borders into place. You will want to center the border so that it extends past each edge of the quilt evenly. The fabric should be face down on the top of the quilt along the edge.

Step Three:
Sew the top and bottom borders to the quilt top.

Step Four:
Pin the side borders into place. You will want to center the border so that it extends past each edge of the quilt evenly. The fabric should be face down on the top of the quilt along the edge.

Step Five:
Sew the side borders to the quilt top but start and stop sewing ¼" from the corners of the quilt top itself. DO NOT SEW ONTO THE OTHER BORDERS. Be sure to backstitch at each end.

Step Six:
Fold the quilt top in half diagonally so that the two edges neighboring corner you are working with are lined up together. I work like I read (from left to right, top to bottom) so let's start with the left top corner. grab and lift the top right corner and fold it over toward the bottom left corner. It doesn't have to go all the way to the bottom left corner. be sure that what was the top edge of the quilt is now lined up with the left edge of the quilt.

Step Seven:
The left border and the top border need to be aligned so that they lay perfectly on top of each other.

Step Eight:
Locate your backstitch and draw a 45 degree angle extending from there toward the opposite side of the border and toward the end of the border.

Step Nine:
Sew from your backstitch along this line. NOTE: This method should give you little or no puckering as long as you sew from the backstitch toward the outside and not the reverse.

Step Ten:
Press the border and it SHOULD lay flat. If not, grab your trusty seam ripper. This is how to make a mitered border. Repeat steps Seven through Ten for each of the other corners.