The first step in engaging more people in the democratic process is to make it a true democratic process to begin with. The way the electoral process is set up and executed is insufficient in representing the democratic spirit.
When the electoral process was set up in the constitution, it made sense given the state of communications of the day, however we live in a much different world in which everyone has access to the necessary information in making an intelligent decision in government representation. The responsibility of the decision should rest solely upon the individuals voting.
Unfortunately, of the Americans that do vote, many feel comfortable voting straight republican or straight democrat because it is easier than doing real research on individual candidates, and so for these people, the change in the electoral process is not necessary. Unfortunately, due to this large number of lazy voters, the people who work hard to inform themselves waste their time because they can't get past the mass of people happy with the two party system. Two parties whose agendas seem to switch roles every few decades or so.
If each of us is to take personal responsibility, it is essential to feel that it is first worth the time. It truly seems as though by the time the public has any choice, so many decisions have been made for them that their choice is merely a flip of the coin between pre-packaged candidates that aren't very different. And in most recent cases, it would seem as though neither tends to take their role for what it is, which is the ultimate representative of the will of the people of the United States.
A few steps have been taken in the right direction, with Maine and Nebraska opting for a proportional allocation of electoral votes in the presedential election. Although this is not ideal, it is about as close as it can get without having to change the constitution (which may need to happen, it was set up to be changed).
So we need to start at the beginning, until candidates and representatives can realize that they are required to accurately represent the will of the people and the electoral syetem is widely revamped, the government will never accurately and precisely represent the people that pay them to do so, and people will be hesitant to take the time to engage in the process.