Complement System is part of Innate immunity. Complement cascades are activated against foreign body, bacteria and viruses. Here is an easy explanation of activation for complement system in human body. The video is illustrative and self explanatory.

 The complement cascade can be activated in 3 ways:

1. Classical pathway 
2. Alternative pathway 
3. Lectin pathway 

 For the full text on complement system: Complement system made easy