The Kitchener stitch is used to join two pieces of knitting together by using a large-eyed blunt needle and sewing in a manner that imitates knitting. It is commonly used to join the toe end of socks so there is no seam to rub on the toes.
Cut the yarn, leaving a tail equal to the amount you would normally need to finish the row
You'll have two pieces to join, one side on each of two needles. Hold the needles parallel, wrong sides together
Thread the end of the yarn through a large-eyed, blunt needle (often called a 'tapestry needle')
Working from right to left, insert the large-eyed, blunt needle in first stitch on lower piece as if to purl and draw the thread all the way through. The working thread should be under the needles each time.
Insert needle in first stitch on top piece from front to back and second stitch from back to front
Pull yarn through and take the stitch off the needles.
Insert needle in first stitch on lower piece from front to back and second stitch from back to front.
Pull yarn through and take the stitch off the needle.
Repeat until no stitches remain. Bring the tail to the inside of the work and fasten off.