THE ANTENNA LENGTH :
The design center frequency of the full-size version (configured as a 3/2-wave dipole on 20m) is 14.150 MHz, and the dimension of 102 ft is derived from the formula for long-wire antennas which is :

TOTAL LENGTH IN FEET = 492 X (N - 0.05)) / F(MHZ)
So we have:

492 x ........

N - 0.05 = 3 - 0.05 = 2.95 ("N" is the number of 1/2 wave lengths)

Continuing with the formula:

492 x 2.95 = 1451.4

1451.4 / 14.15mhz = 102.57 feet total length (51 feet per half)

In practice, since the whole system will be brought to a low swr for use by the transmitter with the use of an antenna "tuner", the antenna is cut to 102ft (31.1m).
In some cases, this is still too long to fit in the required space. In this case, a half-size version, covering 7 to 28 MHz is still very usable. This is sometimes called the "JR" version if bought commercially.

Conversely, some amateurs would like to have 1.8 MHz capability, and have the 204 ft ( 62.2 m ) length necessary for the G5RV antenna.

The antenna does not need to be put up as a flat-top (horizontal fashion), but can be installed as an inverted-V.
If the antenna is raised as an inverted-V, the included angle at the apex should not be less than 120 degrees.
The center of the antenna should be as high as possible, of course, and the matching section should descend at a right angle to the antenna.

THE ALL IMPORTANT MATCHING SECTION :
The matching section may be designed in several ways.

Open Wire :
This is the preferred construction using open-wire feeder for minimum loss, as this section always carries a standing wave on it. Due to the standing wave, the actual impedance is unimportant. 

Ladder Line (Window-type line) :
The next most desirable matching section would be made from window-type open wire line, either 300-ohm, or 450-ohm. This is basically a ribbon line, like heavy duty TV-type twin lead, with #16 to #20 wire, and "windows" cut in the insulation every 4 to 6 inches. The advantage of the "window" line is that the conductors won't short together if the line twists in a high wind due to it's construction.

MATCHING SECTION LENGTH :
The length of the matching section is an ELECTRICAL half-wave on 14 MHz. The actual physical length is determined by the following formula :

LENGTH ( in feet ) = ( 492 x VF ) / f (MHz) ( VF = the velocity factor of the matching section )
The velocity factor is determined by the type of line, and the dielectric properties of it's insulation.
For the three types of line discussed so far, the VF is :
Open wire = 0.97
Ladder line (Window line) = 0.90
"TV" twin lead = 0.82
Note that these velocity factors may differ between various suppliers so it is best that you check the specifications of the type that you use. Also remember that your tuner will make up for any minor differences.

By substituting the VF in the formula, and calculating for a center frequency of 14.15 MHz, you come up with the following matching section lengths :
Open wire = 33.7 ft ( 10.28 m )
Ladder line (Window line) = 31.3 ft ( 9.54 m )
"TV" twin lead = 28.5 ft ( 8.69 m )

Here is the math for those who need an example:

Let's use TV type twinlead in ours.
VF of TV type twinlead is .82

So.....Length in feet for matching section (total) = 492 X .82 / Fmhz =

492 x .82 = 403.44

403.44 / 14.15mhz = 28.51 feet for TV type twinlead

FULL-SIZE, DOUBLE-SIZE and HALF-SIZE (sometimes called the "JR":

28Mhz. On this band, the antenna functions as two "long-wire" antenna, each of three half-waves, fed in-phase. The polar diagram is similar to that of a three half-wave "long-wire" but with even more gain over a half-wave dipole due to the collinear effect obtained by feeding two three-half-wave antennas, in line and in close proximity, in phase.

Construction notes and tips:

1. The matching section is connected to the center of the antenna as with any ordinary dipole antenna, and allowed to descend vertically at least 20 ft or more, if possible.
It can then be bent and tied off to a suitable post or line, and connected to the coaxial cable and run to the antenna tuner.
 
2. At the junction of the matching section and the coax, it is highly recommended that this junction is well sealed from rain, ice, snow, etc. Also provide a strain relief support for the entire junction section to prevent breakage here. This area will be prone to breakage by wind twisting.

3. A good center insulator support to provide strain relief for the matching section is also recommended.

4. Under certain conditions, either due to the inherent "unbalanced-to-balanced" effect caused by the direct connection of a coaxial feeder to the end of the (balanced) matching section, or other causes, a current may flow on the outside of the coaxial outer conductor. This effect may be considerably reduced, or eliminated, by winding the coaxial cable feeder into a coil of 8 to 10 turns about 6 inches in diameter immediately below the point of connection of the coaxial cable to the end of the matching section. The first and last turns should not touch and the coil should be taped securely to help prevent this. Some builders use this, some don't.

5. If you use regular TV type twinlead for the matching section, it's probably a good idea that you do not run much over 100 watts of power due to high swr on the feedline. Do not tape the matching section to a metal mast or pole.

Conclusions based on comprehensive research by VK1OD