ICBM's typically carry payloads of 1,000 kg or more of mass. Most ICBMs used for peaceful purposes can launch into orbit only small payloads. The single best example of this is the Dnepr rocket. The rocket itself can carry 4,500 kg to LEO, but the SS-18 Satan (R-36), from which it is based carries a 20 MT bomb. It's hard to say exactly what that translates to, but one can assume a near linear capacity based off of it's mass, which would give around 6,000 kg when compared to the Agni-V missile.
They also fly a different trajectory. Most ICBMs actually fly at or very near orbital speed, although not in the right trajectory for orbital flight. The Wikipedia article for the R-36 states that it flies at 7.9 km/s, which is actually orbital velocity. Simply re-programming the computer to fly at a more level flight will allow it to achieve orbit.
The other way that is done in the instance of the Minotaur Rocket that Northrop Grumman produces is using the stages to build a rocket that can carry a larger payload in to orbit. They may use two first stages, for instance. Most of the ICBMs use solid rockets, and are vastly overpowered, so carrying two of the stages is totally possible.
The bottom line is, some major software changes are required, and interface with the payload, payload fairing, and possibly a slight hit in mass, but little else is really required to launch an ICBM to orbit. But if you want a higher performance one, then just assemble the stages together from multiple rockets.