One way that has been particularly successful, but not heralded or championed, has been the international peacekeepers of the United Nations. UN peacekeepers, the "Blue Helmets", have been and are stationed in dozens of countries and in between others. Multiethnic, multinational and binational states are thus denied their flashpoints--the source of contact and most frequent source of conflict. This has allowed years to pass, systems and institutions to develop, and in some cases, for bitterness and feelings of hatred to subside to the point a more long term solution has become viable.
Maybe we need to spend some time considering how to bring all those varied groups together in working toward a common goal. History is full of episodes in which diverse people have united in response to a challenge or crisis situation. It would be a huge challenge, but if Americans could come together behind a universal effort to reduce pollution, provide health care for all, end illiteracy - some major, obviously critical issue that would benefit everyone if it were successfully addressed - maybe we would focus on that goal and forget the bickering between smaller groups.
Unfortunately history is littered with failed attempts to achieve the kind of peace and stability that countries like South Africa and the United States have managed (arguably) to achieve. Notable examples include the former Yugoslavia and Rwanda. #2 makes a very valid point in the assertion that the only real way to achieve peace is to make people love their country more than their tribal ethnicity or origin, yet how precisely we work at achieving this is a very difficult question, and will probably take generations to achieve.
South Africa is a study of this desire for unity and peace in progress. As we have seen across a long history in South Africa, the first step is agreeing to respect and honor the other faction(s) enough to talk. The next step is to find a way to trust and believe the other and to provide a reason to be trusted and believed in return. The film Endgame (Pete Travis, 2009), with William Hurt, enlightened this process as it played out in South Africa in the 1980s.
There are many possible ways to maintain peace and unity in such states.
One possibility, particularly when the various national or ethnic groups are relatively concentrated geographically, is federalism. Federalism has the advantage of giving each region a degree of autonomy and self-determination. It can run the risk, however, of creating little enclaves that will eventually want to break away from one another.
Another option is something like what has been tried in Nigeria, with different ethnic groups taking turns in power. In Nigeria, there has been a system in which the two major regions of the country essentially take turns having the president be from their region. This can give different ethnic groups a feeling of being sharing in power. However, it can also lead to each ethnic group ruling only for itself.
The best way to actually have peace is to have groups that are more loyal to the country as a whole than to their own ethnic group or nationality. This is what we have (for the most part) in the United States. The downside there is that it is very hard to get people to feel this way. It generally takes generations to achieve this sort of feeling.