Most of it is encrypted now. But there was a time when you could hear the whole war playing out

Including High VIP conversions.
But if you want to try it here are some antenna plans.
The antenna I used was a 12 turn axial mode helix...Like some of the TV trucks have. The preamp was a a 20Db gasfet from Advanced Receiver Research. The receiver was a Yaesu FRG-9600. The helix antenna is VERY easy to build.
The following dimensions will give you about 16Db gain over the entire 242 to 270Mhz Milsat band:
Diameter of the helix - 14 inches
Circumference of helix - 45 inches
pitch or spacing of turns - 11 inches
If you're within 10% of these numbers it'll work fine.
The helix element can be constructed from refrigeration type copper tubing, 1/4 inch diameter.
The reflector can be anything from chicken wire
If you make it square, it should be .8 to 1.0 wavelengths on a side...so 45 inches will work well.
The polarization is Right Hand Circular.
If you're standing behind the antenna, at the feedpoint end, the turns of the coil should spiral away from you in a clockwise direction. The nominal impedance of the antenna is around 140 ohms. To get a good match to 52 ohm coax, make the first quarter turn at the feedpoint end run parallel to the reflector at about 1/8 to 1/4 inch spacing from it. This will act as an impedance matching transformer and give you a pretty good match.
DO use good low-loss coax. Belden 9913 will give you the best results.
This antenna has a beamwidth of 30 degrees and is VERY broadbanded. Be sure to use a non-conductive boom...hardwood works, fiberglass works much better. PVC tubing has too much sag.
Some of the milsat signals are strong enough to copy with only a ground plane or discone antenna.