You might think it difficult to do, but it really isn't. There's many ways to do this, some quicker than others. You can use Global Positioning guided bombs to destroy all the really important stuff, like power plants, water treatment facilities, communications infrastructure, things like that. But if you do that, it's pretty obvious that you're doing it on purpose.
But, if you want to destroy one without anybody catching on, you've got to be a bit more inventive.
Step 1: Change the culture
In order for a modern country to be modern, it takes a collective desire to make things better for everybody. In order to destroy that type of thinking, create a culture where fucking people is desirable. Perhaps create television shows, where the "hero" is the person who's most likely to screw the group. Maybe you could make a television program about survival, that isn't really about survival, but coming out on top at any cost to the group.
Or, create a musical genre which pushes taking what you want, when you want, while at the same time, advocating violence if anybody does that to you. It might seem a bit anarchistic, and completely self serving, but I'll bet people would buy into it. The concept is basically sound - you get what you want, and get to hurt people indiscriminately. You'd better add a strong "no snitching" aspect to it, because if there were any kind of a hint that wrongful action should be pointed out, this system doesn't work very well.
Step 2: Destroy the valuation of everything
Make things so convoluted, and price structures completely insane, that nobody has any idea what anything is actually worth. Get the price of someting important to everybody, say, oil for instance, to fluctuate so wildly, that nobody can get any kind of an idea what it should actually be sold for. Instead of basing the price on what is, base it on wild, inane speculation. Inflate the price of real estate to incredible levels, without any justification, let it reach a point where it become's unsustainable, just throw your hands in the air when it becomes apparent that's what you did.
Take profitable businesses, put incompetent buffoon's in charge, and let them run them into ruin like a drunken ship captain, or a text messaging addicted train engineer. (step 1 is great for accomplishing this.)
Step 3: Demolish any sense of justice
A great way to destroy a sense of justice, is to make it completely nonsensical and arbitrary. Take a group that have a slim chance of doing harm to the country, and eliminate any and all judicial processes, due to the danger they pose. Perhaps angry Muslims on the other side of the planet. Then, let people off the hook, for prosecutiorial misconduct, when there's overwhelming evidence that what they're doing is a severe, direct threat to the country. Give a couple of corrupt politicians 'get out of jail free' cards. Overstate a possible threat, and blow off actual direct ones. Get people so screwed up about what is lawful, and what isn't, that they just don't care anymore.
Another way to accomplish this, is to take actions that were considered criminal, and debate it. There's nothing that will fuck up a sense of justice, more than this. Pick an action that you once used to vilify other countries, and use it for the same reasons given by the people you vilify. While stupid people won't get it, intelligent one's will suffer from serious anxiety, fear, and a foreboding sense of doom.
This correletes to step 2 - once you can't determine any actual value of things tangible, the value of abstract concepts get just as hazy.
Step 4: Create conflicting laws
This might actually be a subset of step 3, but considering the damage it does, it should have it's own step. Create feel good laws for constituents, and then, other ones that bypass these. Something like a minimum wage, or unemployment insurance. Laws like this will make a politician popular among voters, but it doesn't sit well with the people who fund their careers. So passing laws, thhat bypass the feel good laws, such as free trade agreements, will keep the campaign coffers full. Let's face it - the people you're trying to rule can't afford to put you there,
only the rich ones will do that. So, despite having to waste time passing the feel good laws, you can actually get laws passed that mean something to the people paying for them.
Step 5:Turn information sources into proopoganda machines
Take what people once knew as sources of objective data, and use them to steer opinion. You can make anything look good or bad by doing this, you can make monsters out of jews, muslims, doctors, you name it, you can make it look bad. Inversely, you can make things that are known to be bad, and make them look terrific. Things like financial instruments based on unachievable ends, and insurance for such.Put the bedrock for something like this on 'contract law,' and even though those contracts were built on lies, they have to be inforced. (see steps 1,2, and 3)
Once people can't deternine fact from spin anymore, they become as pliable as silly putty, or so confused, you can pretty much do whatever you want to them. They'll be so busy sniping at each other over the spin, that the actual facts get overlooked. (steps 2 and 3 again)
Step 6: Destroy education
Nothing is better for destruction, than dumb, ignorant people. The dumber they are, the easier it is to use them. You can convince them that shooting doctors who save lives, is actually a good thing. That the taxes that keep police on the streets are bad. They'll believe that the good of the group isn't important, as long as they're getting what they want - when they aren't getting anything. You'll get people who can't construct a sentence at a third grade level, to push your agenda for you. They'll see commercials on television, advertising loans to anybody, and actually buy these loans, for their 'inherent value.'
Step 7: Use technology
Create a system of interconnected computers, allowing people to feel like they're actually accomplishing something, while spinning their wheels. You can support war, without getting out of your chair. You can complain about government, without doing anything about it, other than typing snarky, ineffective ranting. (yes, I realize the irony.)
How can you accomplish this? Develop a government that's built on deception, corruption, and collusion. One in which a supposed 'representative of the people,' openly complains abut the smell of the tourists, having created the conditions that cause those people to smell. One where corruption isn't seen as corruption, but political ethics. One where the elected, are funded by the people we elect people to protect us from.
Now, you must ask who's responsible for this, and what do we do about it? We're all responsible. And the only way to get it back, is to hold people accountable for their actions; be they government or corporation. Turn off the propoganda machine, until they start acting the way jounalists should. Demand that politicians stick to their promises. Demand that the law be inforced, uniformly, without any political interference.
It's not a cure all, but it's a start.
Flame away.