Counter-insurgency warfare is not for the most part done "kinetically", which means conventional warfare. It requires more subtle military use and many civil programs to defeat the insurgents.
Insurgency can be viewed as fish in a pond. The water in the pond is the residents of the area with the insurgency, and the fish are the insurgents. The insurgents rely on the people to get supplies and manpower, or in the illustration, the fish need the water to survive. This means you'd have to get rid of the water to kill the fish. The only way is to reduce the support for the insurgency, and that is through the people.
To reduce the support for the insurgency, the people must have the basic requirements for human life, like shelter, food, water, etc. Extra requirements are security, and the higher orders of Maslow's Heirarchy of Need. Also, the side that is fighting the insurgency must also have detailed knowledge of the people's culture in order to de-escalate the situation, rather than escalate it (which is by blowing things up, arresting everyone in sight, etc). Psychological warfare is very important, as with gaining the moral high ground. If the people are happy, then the support for the insurgency decline. If they are not, then they will fight.
But this topic is very complex, because social, political, economical, and military arrangements must be carefully mixed to make for an effective "combined arms" solution to insurgencies. But if you wanted one word to counter guerillas: "de-escalate"