I think that such a question becomes one that strikes at the essence of the democratic process. Certainly, one does not make majority based decisions as a "zero sum" calculation, where one side's views dominate the other. Rather for the most part, democracies have seen that when consensus does reign, it still must acknowledge the voices of the vanquished in future decisions. The power of the majority is one that does have to reckon with the force of a vocal minority. American legislative history has addressed this. Even with overwhelming majorities in both chambers of Congress, parties in power still have to balance the needs of "the other side" for these are voices in the political process that must be heard and acted upon, to a certain extent. This creates the foundation of being able to seek majority rule without the oppression of the minority in the process.
You ask if we limit the the rule of the majority, are we still a democracy. To me, if we fail to protect the rights of minorities, we are also not democratic.
These are two aspects of demcracy that are fundamentally in tension with one another, but they are both vital to democracy.
As far as what you can do, the only thing you can really do that will make a a long-term impact is to change the people's minds so they do not want to oppress the minorities.
This has already, for the most part, happened with non-whites and women in the United States -- majorities don't really want to oppress them anymore.
The first answer is right to say that you can try to protect rights in those ways, but those ways will not really work over the long term unless enough people change their minds and stop wanting to oppress the minorities. For example, there were safeguards like the ones he talks about for blacks even during the time they were being segregated. It's just that the safeguards didn't work.
There are a multitude of protections that can be built into any democracy that protect the minority. One, you can add constitutional rights that supersede majority will - like the Bill of Rights in the United States. All laws passed by majority rule are subject to those amendments and the Constitution.
Second, you can build in procedural rules like the filibuster, or calls for reading of a bill, amendments to a bill, etc. that slow down the process and give the minority a limited form of veto, although this can obviously be abused to the point where the democracy is threatened.
Third, because one group is the minority in a country overall, it does not mean it is the minority locally, meaning they can still elect candidates and have some local control over their own lives, allowing them to still live according to majority rule without being oppressed, at least directly, by that majority.
Take Dearborn, Michigan as an example, which has one of the highest populations of Iraqi-Americans in the country. Clearly a religious and ethnic minority, but with enough local numbers to still control their local governments to a reasonable extent. Since their religion is protected by the 1st amendment, they are also protected by the courts.
** In response to pohnpei's statement -- it is true the Constitution failed to protect blacks for nearly a hundred years - the system worked as it should have, but popular will was against it in the South. To be fair though, the court ruled as it should've in favor of minority rights in Brown vs. Board of Education in 1954, and then the order was enforced against the majority will of southerners, by a President who didn't favor minority rights (Eisenhower). So while slow, cumbersome, and often unsuccessful, in this case the system and the protections within it did in fact work.