The Kitchener Stitch - From your friends at The Yarn and Fiber Company.

A simple and essential technique for closing the toes on socks, joining scarves etc. Hated by many, loathed by some, but in practice one of the simplest and most elegant ways to finish any garment where two sets of live stitches need to be joined.

SET-UP
1. Divide stitches between two needles evenly.
2. Thread yarn onto a suitable size darning needle.
3. Hold needles such that working thread (and darning needle) are to the right.
4. Pass needle (and yarn) through first stitch on front needle right to left (as if to purl).
5. Pass needle (and yarn) through back needle, left to right (as if to knit)

KITCHENER STITCH
6. Pass needle (and yarn) through first stitch on the front needle, left to right (as if to knit)
7. Slip first stitch off front needle
8. Pass needle (and yarn) through next stitch on front needle, right to left (as if to purl) - leave on needle
9. Pass needle (and yarn) through first stitch on back needle, right to left (as if to purl)
10. Slip stitch off back needle.
11. Pass needle (and yarn) though next stitch on back needle, left to right (as if to knit) - leave on needle
Repeat kitchener stitch, steps 6-11 until all stitches are off both needles

Tip: Do not pull stitches tight, stitch tension should match that of knit stitches. Keep working thread between knitting needles, avoid wrapping it around a needle.

Sequence is:
Purl Front Needle, Knit back needle (set-up) then
Knit Front Needle and slip off
Purl Front Needle
Purl Back Needle and slip off
Knit Back Needle

GRAFTING (using Kitchener Stitch) to acheieve finished garment on both sides.
Follow instructions as for regular Kitchener stitch, steps 1 through 5, but make sure you start with a knit stitch. If you cannot and must start on a purl stitch then on steps 4 and 5 knit and purl instead of purl and knit. This technique will not give you a perfect join as there will be a half stitch jog when switching between knits and purls but I have not come across anything better yet!
6. Pass needle (and yarn) through first stitch on the front needle, as if to knit for a knit stitch, or as to purl to a purl stitch.
7. Slip first stitch off front needle
8. Pass needle (and yarn) through next stitch on front needle, as if to purl for a knit stitch or as to knit if a purl stitch. Leave on needle.
9. Pass needle (and yarn) through first stitch on back needle, as if to purl for a knit stitch, or as to knit for a purl stitch.
10. Slip stitch off back needle.
11. Pass needle (and yarn) though next stitch on back needle, as if to knit for a knit stitch, or as to purl for a purl stitch. Leave on needle
Repeat kitchener stitch, steps 6-11 until all stitches are off both needles