Not everyone will agree with this explanation but here goes

I use front tilt and swing to rotate the plane of focus to more closely line up
with the plane of the subject. Back swing and tilt will do the same but these
movements will also change shapes and size relationships between objects.

Tilt/swings do not really enlarge the dof area as much as they align it with
the pplane of the subject.

As an exercise take your camera out to a road and set it up level front to rear
and left to right. Focus at an approx mid point in the road as it moves away
from you. The bottom of the road (at the top of the gg) and the distant section
of the road (at the bottom of the gg) will not both be in focus at the same
time. Now, ever so slightly and slowly begin titling the front and see what
happens. This will take some practice but the amount of tilt required will be
less than many people think.You may have to do a little re-focussing as you
tilt. Just go slow and watch the gg and see what happens. A 4x loupe will help.

Here is some suggested reading

User's Guide to the View Camera by Jim Stone

Using the View Camera that I wrote

Large Format Nature Photography by Jack Dykinga

All three are books you can get from Amazon.com

steve simmons

You'll find you need VERY little tilt to acomplish what you need for most
landscape shooting. The mistake most newbies make is thinking they need to
tilt it a bunch to see anything. It's not hard to modify the front standard
to get a little down tilt without resorting to the bed drop ordeal.

"Neil Purling" <neil@sextant.karoo.co.uk> apparently said:

Tilts, and their horizontal counterpart, swings, do not increase
the zone of sharpness.  What they do, is to change the plane
of sharp focus.  With an untilted lens, a camera can sharply
focus a plane that is parallel to the lensboard only.  When
the lens is tilted forward, the plane of sharp focus also tilts.
Do a search for "Scheimpflug" and you'll get all the details.

When your subject consists of essentially the ground
between you and the horizon, with maybe a mountain in
the background, tilts let you align the plane of sharp focus
with the subject.  The result is the appearance of immense
depth of field, even with the lens wide open.

Juggling is a good analogy.

That's the usual way.  Use a loupe on the groundglass to
fine focus a point in the foreground, then tilt to bring a
far point into focus.  Go back and refocus the near, retilt
for the far.  After a couple of iterations things will look good.

Yup, you've figgered it out.  The problem there, is that every time
you tilt (with the bed dropped) you'll unfocus the whole image,
so there will be more putzing around.  Some people have also gotten
around the Graphics lack of native front tilt by reversing the
front standard.  Then, of course, you lose the ability to drop
the bed, unless you do some hacking on the standards.

With a camera that tilts from near the rail or
bottom of the standard, I generally begin with the
background (D-far), since a forward tilt inclines
the plane of focus toward D-near (i.e., the axis
of rotation is not centered.) This is not an exact
science in my experience especially with a field
camera, unless you use a camera (like Sinar) that
tells you the exact degree of tilt needed based on
a two point focusing of D-near and D-far. Refocusing
and/or slight retilting will be necessary.

In other words doing this visually usually requires
some trial and error experience. And as you're altering
a parallel plane of critical focus (from a zeroed camera
to an inclined front standard), unless your subject is
flat (receding two dimensionally) you will have objects
that fall outside the adjusted inclined plane of
critical focus. This is due to the Scheimpflug Rule.
In other words you are actually fousing on a series of
objects that vary in distance top to bottom and will
also be altering the near and far limits of depth of
field. Meaning since depth of field space is actually
curved, your new D-far (most distant object you want
in acceptably sharp focus) will be somewhere in the
middle of the image area beyond the inclined plane of
focus.

I know that sounds a bit abstract but once you adjust
the plane of focus for background and foreground,
you'll need to recalulate your depth of field based on
a new D-far.