UPDATE Dec. 28th, 2009: I leave the text below essentially intact for reference. Also, it is pretty much accurate, to this day. For updates and more extensive information, consult The Knucklebook.
Unlike a four-seam or two-seam fastball, the knuckleball has a history of not
quite being everything the name implies.
Originally thrown by Toad Ramsey, the grip was an odd one, even by today's
standards. He severed a tendon in his middle finger as a youth, so he simply
placed it on the ball, and gripped the ball wide (apparently for comfort and
stability) with the neighboring fingers. Try this yourself and you'll see that
the ball was gripped more to the sides than along the top. This looked and acted
more like a forkball, little over-the-top rotation and a lot of sink.
Ponder that, and you'll understand the rest of this explanation.
A knuckleball is simply a ball thrown with little rotation, with one or more
fingers curled so as to grip with the knuckles, fingertips, or sides of the
fingers. Nothing more.
Here's a copy of the back of a Goudey Premium, 1939 vintage, explaining how one, a.k.a. a "floater" is thrown. For basic instruction on how to throw a knuckleball, not much needs to be said beyond this, except for the fact that most grips nowadays are with the fingertips.

It can be gripped anywhere, any way, with success. Unlike four-seamers or
two-seamers, there's no right way, no standard placement on the ball, no
standard number of fingers in contact with the ball, no standard location for
the thumb or placement on or next to the seams. Knuckleball pitchers always say,
"This is how I throw it" not "This is how you should throw it".
Funny things happen with a slowly-rotating ball. A large pocket of swirling
air develops behind it, and how the rotation is will change this pocket, larger,
smaller, back and forth, and this pocket pulls against the ball, sometimes in
one direction for a moment, then another. This pocket, or wake, is disturbed by
air moving over seams or smooth surface. Air drags over smooth surfaces, but
seams produce lttle swirls behind them, which act like ball bearings to allow
the air to pass over easier and faster. Therefore, the orientation of the seams
alternately trips and fills this wake behind the ball, giving it whatever action
occurs.
Another interesting thing is the fact that this wake causes a lot of drag. If
there's little side rotation, but none across the top-- or forward rotation
across the top-- you will get a hard sink. This is the concept behind the
forkball, splitter, or foshball. Those who throw these pitches try to produce
some so-called "tumble", simply little rotation. Well, guess what you're trying
to produce with a knuckleball: the very same thing!!!
Add some side rotation, and all you get is the sink. Almost eliminate side
rotation, and you get side movement. In that respect, if one threw a forkball or
splitter with very little side rotation, it would wobble from side to side. So
you got knuckleball action without any grip involving the knuckles.
Therefore, understand that the side-to-side wobble and sink of a knuckleball
can be created by grips other than the standard knuckleball grip.
Eddie Cicotte invented the knuckleball grip, but by no means invented the
first grip that could produce knuckleball-type movement. In fact, photos of his
grip show a variety, all with the simple intent of MINIMIZING rotation IN ANY
DIRECTION. This is important to understand. It appears that all he was trying to
do was to reduce rotation, period, and that any side-to-side movement was an
added bonus.
Looking at his grip, I find it very easy to grip the ball with my small hands
and get the knuckles right down on the ball! At times, he gripped the ball on
one side with his thumb and the other side with his pinky finger or the side of
one or more curled fingers. Try this and you'll find you are only holding the
ball at two points, one on each side, and the fingertips can easily curl under
to place the knuckles atop the ball.
It's apparent that later practitioners gripped the ball more top-to-bottom,
with fingertips opposite the thumb, which is hard to do without large hands.
The thing to especially note is that the knuckles were placed on the ball
(and with later grips, the fingernails) apparently so as to GENTLY FLICK THE TOP
OF THE BALL FORWARD. If this keeps spin limited, cool, you have the sink and
probably some wobble. If you produce some forward topspin, you're just getting a
fall-off-the-table sink. (This is why Eddie Cicotte called it a "dry spitter"
at one point.) Mike Mussina throws a hard one with topspin which curves, if you put some slight side-spin on it or release it off to the side a little on an angle. If you're a pitcher, EITHER is cool!
All the early practitioners were apparently trying to do is throw something
that moved by surprise. Period. They didn't sweat a little rotation, they didn't
sweat humidity or air pressure or trimmed fingernails. Cicotte called it a
knuckleball ONLY because curled fingers were a part of the grip HE DISCOVERED BY
EXPERIMENTATION WORKED FOR HIM.
Some pitchers say, "thumb on the seams". Some say "no thumb on the seams".
Some say two fingers, three fingers, one finger, some on the seams, some next to
the seams, some get knuckles down, some only fingernails, some dig in the
fingernails, some throw it like a fastball with the index finger curled and get
a slight spiral action which produces a so-called knuckle-curve which does curve
as well as sink.
Here's some info from John Phillips every struggling knuckleball pitcher must study carefully:
Take a look at this picture. This is the exact moment when the ball is released from a knuckleball grip (Tim Wakefield). In order to prevent excessive spin, the last three fingertips that touch the ball (all at the same time, by the way) are the thumb, index finger, and middle finger. They push the ball out (kind of like flicking those three fingers to close a door) all at the same time to create a "triangle" of pressure, which prevents spin. The ball rests against the palm and that's what allows the forward momentum of the arm to create speed on the ball (fingers are not strong enough to hold the ball away from the palm when throwing). Once the momentum starts going forward, the ball starts to fly away from the palm just by inertia and gravity. By pushing the fingers out at just the right time, the three fingertips keep the ball from spinning. Trying to release the ball with just two fingers always results in too much spin ... the thumb has to be there as well.

I was really struggling with throwing it with any consistency until I really studied two slow motion videos of Wakefield. I was releasing my thumb and stabilizer fingers and pushing with just the index and middle fingers. Once I added the thumbtip back in ... BINGO!! What's frightening is that I can consciously throw a ball with absolutely no spin if I so desire. Now I can throw with little rotation (top spin, back spin, side spin) just by positioning the fingers slightly differently on the ball. It was a pain to master, but now seems so simple.
To get a perfect knuckleball grip, hold out your thumb, and the first two fingers. Then place your thumbtip, and first two fingertips on the ball all at the same time, and not on any seams. Then push the ball with your left hand into the palm of your right hand, leaving your fingertips in place. Your fingers will curl. Then use your ring finger and/or pinky to gently hold the ball so it won't slide out the side of your hand. Some people use only the ring finger, others use just the pinky and place the knuckle of the ring finger against the ball. It's really whatever your comforable with and whatever works. Most people try different grips until they get one to work consistently.
Then rev back and throw it. Remember, don't snap your wrist down (like a fastball) and don't push the ball (like a shotput). It's a relatively normal throwing motion. Let the forward momentum of your arm create speed on the ball (as it rests against the palm), and then let your fingers push the ball out when the momentum shifts to the release point. You'll find that you release the ball a little earlier than if you were throwing a fastball, mainly because of the grip. You'll take your ring and/or pinky finger off of the ball just before you release and just as you start to push the ball out with your fingertips.
I was throwing a bunch of these this weekend at Mom & Dad's house and was getting some wacky stuff to happen that I could visibly see. Wiggles, hard drops, hard breaks sideways (both directions).
Thanks, John. As you can see, experimenting and carefully observing what's going on and making a consistent adjustment will get you far, even if all you know about it is printed on the back of a Wheaties box.
Phil Niekro had one set grip, but he threw it with three different arm angles
and three different speeds. Now that you know the above, you might find not one,
but several other grips you can use in your own efforts! Or, maybe a new one
that works for you! I've said that the knuckleball is not a single pitch, but an
assortment of pitches, or a class of pitches, like the fastball class. Work on
that and you might find success you didn't think possible.
It has been scientifically measured that the most action of a knuckleball can
be expected at about 72 mph or so. DO NOT GET HUNG UP ON THIS. You can throw
something ugly and spinning, by accident or otherwise, at 90 or 30 and still get
a strike or an out. Besides, being a pitcher, one of your cardinal rules is,
"whatever you throw, upset the batter's timing and swing".
Many knuckleball hobbyists can't throw it very fast. You should have sound
mechanics to be able to throw a fastball into the 70's before you can expect a
good knuckleball. DO NOT MISUNDERSTAND THIS. I said, "mechanics", not "velocity"
or "strength". A little leaguer can have good mechanics and cut loose with a
high-arc knuckler that has no movement but that's a real killer. Continuing with
those good mechanics as they grow, their speed will increase, and more movement
will develop, but you must have good, smooth, consistent mechanics FIRST. NOBODY
can throw one, trying to push it like a shot-put. That's not how it's thrown.
Notice that it's not really thrown much different from a fastball.
Armed with this information and a lot of practice, your job is to keep the
spin down. Your job is to throw unhittable pitches. Fast, slow, medium,
over-the-top, three-quarters, sidearm, submarine, knuckle-curve, topspin sinker,
gripped left-right with thumb and pinkie, three-, two-, one-finger on top, nails
dug in, flick the fingers, don't flick the fingers, grip the seams, don't grip
them, NONE of these is THE ONE SURE WAY to throw... but play enough with them,
and you may end up with an assortment of speeds, arm angles, grips, and
movement, any and all of which you can call a knuckleball... and maybe a Hall Of
Fame career.
There's a few sites online that make and sell oversized mitts, which may help, but they'll naturally be heavier and harder to handle on a throw to a base. You can warm up for a knuckleball pitcher by wearing the larger mitt and a wrist or ankle weight on your wrist for a couple of minutes. This'll get you better adjusted to hanging that larger mitt out there.