The same as they deal with any other guerrillas.

For practical theory, read Galula's Counterinsurgency Warfare: Theory and Practice.

For a more hands-on guide, read the USMC's Small Wars Manual.

For doctrine on how the US or a US-like force approaches it, skim Army Field Manual FM 3-24, Counterinsurgency Operations.

For examples of how to utterly fail at it, read the past decade of headlines, or read up on the French-Algerian war.

Guerrillas need, need, need a sympathetic populace. It doesn't have to be a majority, but they do need somewhere to fall back to and draw supplies from (that place might be logical instead of physical: churches/redheads/anime clubs/whatever). However, as long as they have that stronghold, it really isn't possible to destroy the movement (technically it is, in the same way that France technically pacified the Casbah. However, I am not aware of any non-genocidal examples where this was ultimately successful). Mao wrote extensively about this, but I don't recommend reading his work as casual research; it's too dense.

So, winning a war against guerrillas is almost entirely a matter of removing their popular support. Raiding/airstriking/assassinating individual guerrillas can help with this (because it's hard to make cogent arguments/carry out threats/govern anime utopia when you're dead), but it also tends to win new converts faster than you can raid them. And it's expensive. Instead you're looking at convincing the populace of a couple points:

1. Your vision is good
2. Your vision is achievable
3. Your vision is sustainable

If you can hit those three points, you basically win, and are into mop-up. But there are some complexities. E.g. even if the new democracy works while the US is around, you can't hit point 3 unless the US will always be around (hah) or you can make people believe that the new democracy will work even without US help.

Anyway, this topic has killed entire forests of trees, this is a tiny, paraphrased summary.

The same as they deal with any other guerrillas.

For practical theory, read Galula's Counterinsurgency Warfare: Theory and Practice.

For a more hands-on guide, read the USMC's Small Wars Manual. Or Greene's The Guerrilla — And How To Fight Him.

For doctrine on how the US or a US-like force approaches it, skim Army Field Manual FM 3-24, Counterinsurgency Operations.

For examples of how to utterly fail at it, read the past decade of headlines, or read up on the French-Algerian war.

Guerrillas need, need, need a sympathetic populace. It doesn't have to be a majority, but they do need somewhere to fall back to and draw supplies from (that place might be logical instead of physical: churches/redheads/anime clubs/whatever). However, as long as they have that stronghold, it really isn't possible to destroy the movement (technically it is, in the same way that France technically pacified the Casbah. However, I am not aware of any non-genocidal examples where this was ultimately successful). Mao wrote extensively about this, but I don't recommend reading his work as casual research; it's too dense.

So, winning a war against guerrillas is almost entirely a matter of removing their popular support. Raiding/airstriking/assassinating individual guerrillas can help with this (because it's hard to make cogent arguments/carry out threats/govern anime utopia when you're dead), but it also tends to win new converts faster than you can raid them. And it's expensive. Instead you're looking at convincing the populace of a couple points:

1. Your vision is good
2. Your vision is achievable
3. Your vision is sustainable

If you can hit those three points, you basically win, and are into mop-up. But there are some complexities. E.g. even if the new democracy works while the US is around, you can't hit point 3 unless the US will always be around (hah) or you can make people believe that the new democracy will work even without US help.

Anyway, this topic has killed entire forests of trees, this is a tiny, paraphrased summary.