Needle Knot Method I
5" doll needle
Hair cut to length wanted (approx. 6" to 7")

Thread a needle with 15 to 20 strands of hair, and knot the end.  From the neck opening, insert the needle through into of the holes in the scalp, and draw the strands up through the hole.  Pull until the knot is tight against the inner scalp.  Work in a circular pattern until all holes are filled.  This method doesn't work well when rerooting a part, too many knots everywhere.  Depending on the kind of hair used, the knot can be fused with a flame before inserting the needle into the neck opening.  Or not!  This does result in a crunchy head, which is not my preference.
(Fashion Doll Makeovers)²

Needle Knot Method II
5" doll needle
Needle threader, notched
Hair cut to length wanted (approx. 6" to 7")

Thread a needle with 15 to 20 strands of hair.  (It helps me to dip the ends in water to hold the strands together.)  Pull the needle down into the scalp and through the head, coming out the neck opening.  Remove the hair plug from the eye of the needle.  Repeat, then three or so plugs together into a knot at their end.  Pull the hair plug back through the holes from the scalp side until the knot catches.  As above, the knot can be fused with a flame before pulling it back through.  Or not!  This puts the flame close to the doll's head, besides making the result crunchy.  Again, this is not my preference.
(Barbie Bazaar March 1997)¹

One Needle Anchor Thread Method 
5" doll needle
Polyester thread (I use Maxi-Lock 100% polyester) 
Hair cut to double the length wanted (approx. 12" to 14")

Put the needle eye first into the first hole of the head (usually at the temple).  Take a couple of yards of thread, double it, and thread the needle with the loop end.  Pull the needle back through the hole, and the looped end creates the first eyelet.  Insert 15-20 strands of hair halfway through the eyelet.  Pull the thread from the neck until the hair is securely in the hole.  From here on, the thread forming the eyelet that secures every tuft of hair will be doubled.  Poke the needle eye first into the next scalp hole.  Fold the two threads forming an eyelet and thread them through the needle's eye.  Pull the needle back through the hole, and the loops create the second eyelet.  Repeat the process of inserting the hair halfway through the eyelet, and pulling the thread back through the hole, drawing the hair down with it.  Continue until the head is completely rerooted.  To finish, bring each of the two threads up through a different (created) hole, knot the threads together several times, rethread the needle, and take the threads back down into the head through a third created hole.  Tie the threads off and cut them inside the neck hole.
(From dollraves website, no longer online.)

Punch Method
This may be a fast way to reroot, but I don't trust the hair to stay rooted, certainly not when it's combed.  Snip off the tip (only) of a needle eye to use as a punch tool.  Snip off the sharp point, then poke that end into the eraser of a  pencil.  (A very fine latch hook may be used instead.)  Catch about 15-20 strands of hair in their middle and poke them down into a hole in the scalp.  I don't use this method, but Bazaar dedicated an entire article to it, so I've included it here.
(Barbie Bazaar July 1993)¹