The first mission, you get four rookie soldiers, and combat the first wave of aliens as they invade.

You are intorduced to the gameplay with optional help and hints, and it is usually not hard to beat this mission.

The second major mission comes much later, when you assault the alien base. This mission comes after months (in-game) and you should have laser weaponry by this point. Most players also use MEC (Mechanized Cybersuit) Troopers, as they have high health and heavy weaponry.

 

Soon after the Alien Base assault mission (About one month in-game) The aliens come after the XCOM HQ and assault it in a heavy raid. This mission is very difficult, as you don't get to pick which soldiers you use. The game picks some of your higher-level troops, and some of your rookies and has them defend the base and more troops get through to help you defend the base.

Later in the game (If you're running the Enemy Within expansion) you get the opportunity to assault the terrorist cell EXALT's base of operations after obtaining sufficient intel on the location. You get to fight a large volume of enemy troops in their command room, an evil reproduction of XCOM's command room.

The final mission is the culmination of all the fighting, taking place on the Alien command ship, as a creepy alien voice whispers to you about the gift (Referring to psionic powers that some soldiers may have). This is the only mission where you fight every enemy in the game, ending with the alien leaders, who, when killed, trigger the end of the game, with the squad sacrificing themselves to save Earth from the command ship self-destructs.