ICBM, Inter-Continental Ballistic Missile, is the term used for land-based long-range missiles, with a range exceeding 5,600 km. They are constructed much like launch vehicles for civilian satellites: A two- or three-stage booster burns for a few minutes, and accelerates the payload to a velocity of 6-7 km/s. (This corresponds to Mach 20 at sea level. For comparison, the escape velocity of Earth is 11 km/s, and minimum orbital velocity is 8 km/s). The payload then travels in a normal projectile motion parabola for about 20 minutes, reaching a maximum height of about 1,000km. During this time no substantial course corrections can be made, which shows the need for very high precision guidance during the boost phase. Modern systems carry a small additional stage, a "post-boost vehicle", to make minor adjustments in mid-flight.
The "payload", of course, consists of nuclear warheads. Older systems could only carry one warhead per missile, but that changed in the early 1970s when the Minuteman III introduced MIRV. Using MIRV, the payload consists of several separate reentry vehicles (RVs), which are released while in space towards separate targets. Upon reentry into the atmosphere, the warheads are slowed down by air resistance from 6 km/s to subsonic speed, and to minimize the imprecision from wind drift the reentry has to be abrupt (hence the familiar acute-cone shape of the reentry vehicles). That gives little time for heat dissipation, so the RVs must be shielded by advanced materials that can insulate from temperatures of several thousand °C without eroding. The energy released during the braking is enough to ionize the air and surround the RV with a plasma sheet, so that its path is traced out by a a pale shining, highly visible ionization trail.
ICBMs of the latest generation as exemplified by the LGM-118 ("MX" / "Peacekeeper") or RT-23 ("SS-24 Scalpel"), apart from being horrible weapons of global holocaust, are quite neat. These two missiles are huge, about 20m and 100ton. (twice the size of a typical SLBM - land based missiles are not constrained by having to fit in a submarine). They have a range of about 10,000km (for comparison the circumference of the Earth is 40,000km), and a total throw-weigth of 4 tons distributed on 10 separate RVs and the post-boost vehicle. The warheads are delivered with a CEP of 90m and 200m respectively, an amazing acuracy considering the global distances involved, but nessesary for their intended limited nuclear war anti-silo role.