Warfare is generally for groups or clans. It is very hard to kill off a country by yourself. Not only does it take time it costs military, money, resources and probably lots of civilians and land. If you however do need to get in war there are many mediums into killing off or crippling a country. You can do this through spy operations, special attacks and missiles. *REMEMBER* warfare should only be used when deemed necessary or when a country poses a big threat to you. Noting that clans will happily kill off your country if you decide to retaliate or hit their countries with several LG's, missiles, harmful spy ops or special attacks.
Declaring War Attacks can be made at any time without any formal declaration of war. However, oftentimes you may find that you cannot attack another country because they are protected by GDI. By Declaring War on a country, you automatically can attack them without regard for GDI. Additionally, you gain a +10% bonus against any country you declare war with. However, they will also be able to attack you without regard for GDI, you can only make peace after 48 hours, and War costs $10/acre for each turn you are at war (included in Alliance Expenses). You may only be at war with one player at a time.
Guerilla Strike Using covert strategies, this attack sends only troops to attack and plunder enemy lands. Because of the surprise factor, only opponent troops can fight back. If you are able to penetrate opposing defenses, you will kill a significant portion of your opponent's civilian population and be able to capture a portion of their food reserves.
Bombing Run Sending a fleet of jets over enemy lands, your army will face defenses consisting only of turret fire. If you can penetrate those defenses, your bombs will both kill off civilians and leave behind a portion of your opponent's buildings in ashes.
Artillery Barrage Pitting your tanks against your opponent's, this military strike focuses primarily on destroying enemy structures. While your opponent will not lose land even if you succeed, a significant portion of their buildings will lie in pieces.
Nuclear Missile Launching a nuclear attack requires that you have discovered a nuclear missile. While all countries have a chance of producing a weapon each turn, technology can help to assist in developing more of these weapons. Launching a nuclear weapon will destroy a portion of your opponent's land. The only defense against this weapon is the SDI system, a product of technological development. 

Chemical Missile Similar to the Nuclear assault in terms of missile development and SDI protection, the chemical weapon focuses primarily on an enemy's population. While it also destroys some land, chemical weapons kill off a portion of an opponent's civilian population, reducing tax revenues until that population is rebuilt. This is the most easily developed missile technology. 

Cruise Missiles Launching Cruise Missiles at an opponent's military installations is an effective way of destroying military of all types. These missiles can help soften up an enemy before invasion.