The only way we can achieve a society with greater liberty and less government is through education. To be clear, this is not about formal education, but about people understanding the benefits and morality of a libertarian society.
The only way that a government can have significant power is if a majority of the people consent to it. The people don't have to go out and be cheerleaders for the state, but they have to at least be tolerant of the state. Most people have gripes about the government in some fashion, but most will also admit that we need government. And these are not just minarchists who think we need a government that only protects life and property and enforces contracts. These are people who generally accept state-run education, Social Security, and various other government programs.
If a majority of people no longer consent to the state, then it will not last for long, regardless of elections. In the U.S., there are over 300 million people. There are only 535 members of Congress. Even if we count all of the government employees, it is still a fraction of the total population. And it is safe to say that a lot of government employees are not there because they love government but because they found a job that pays them money.
I think there has already been a shift in the thinking of many Americans. I think it is for a combination of reasons. The last two Ron Paul presidential campaigns and the internet are the biggest reasons. Another contributing factor is the bad economy, coupled with long and wasteful wars. With all of these things combined, there are more libertarians today than there probably ever have been in history.
The libertarian crowd is still small relative to the population. There are not nearly enough people to drastically reduce the size and scope of government. But the increasing numbers are having an effect, even if it is hard to see. A good percentage of the new libertarian crowd is young adults. They tend to have a more open mind, they get much of their news from the internet, and they can be influenced easier. There are younger people I have met who turned into libertarians within months.
It is important to remember that most people will not be transformed overnight. Most won't even be transformed over the course of several months. You never know what discussion or article or book might be a trigger for someone to open their mind and explore and start the journey.
I think it is important to not go for any home runs. You are not likely to ever persuade someone to become a hardcore libertarian with one or two discussions. The person may say he agrees with you, but you know deep down he does not feel as strongly about a certain issue as you do.
In most instances, the best you can hope for is to chip away at someone's beliefs. You have to remain consistent and principled in your own beliefs. If you are having a discussion with someone and you don't remain consistent, he will likely see it, whether he challenges you on it or not. The best thing you can do is to make him think and make him want to do more research on his own time. There are rarely instant conversions.
Even if you pull off a miracle and have an instant conversion with somebody, he will probably not be a very good representative of libertarian theory at that point. He would still have to go through the education process. If you have been reading libertarian literature for years now, there is probably a lot you take for granted. Think about all of the brainwashing that must be reversed. Think of all of the history lessons that must be retaught. Think of all of the economics that must be corrected.
I have also suggested in the past that you don't try to convert family members. It is probably the hardest thing to do. You will likely get frustrated. Your family members know your faults and will likely see your political stance as a fault. If a family member wants to argue about politics with you, the best way to convert the person may be to have them read a particular article or book. At least they will see someone else as the authority on the matter and not you.
In conclusion, you can do your part in getting a more libertarian society by helping to educate others. This doesn't mean being pushy or getting into arguments. It means helping people open their minds. It means chipping away at their long-held belief that we need government. You will not hit home runs. You must take small steps and let each person take the journey on their own time.