First, how can the human race survive intellectually. By this I mean how can the accumulated knowledge of the species be not lost in another potential Dark Age. Why start here? Because any plan to preserve the human race must include the provision that any other plans might fail. And this aspect is the most readily achievable, the easiest to implement, and the most likely to be necessary (or at least beneficial). Norway's seed vault is a reasonable model for the idea, except that this ark would be storing information about how to rebuild society as needed.
They key, as always, is to determine what information needs preserving, and how best to preserve it. Addressing the latter: electronic non-magnetic media (DVDs) might be good for mass storage in small volume, but it runs into the obvious problem if also requiring compatible hardware to retrieve and display the information. To offset this, hardcopies on some durable material (longer lasting than paper) would need to be preserved along with the electronic media. At the very least, these hardcopies would need to include all essential information necessary to access the electronic media, including instructions on how to build the data readers and how to provide the power necessary for their operation. Within the target 100 years, actual data retrieval equipment could also be stored (based on a renewal power source, such as solar or hand-crank). However, for longer periods, there is no reasonable likelihood that such equipment would survive.
The second aspect of this is what information to store. As noted, part of this includes the requirements for how to get at the rest of the stored repository. However, mere data access methodologies are not sufficient. Assuming this data library was needed to recover from some global disaster or Dark Age, people would still need to survive during the intervening time necessary to access the rest of the data. Therefore, as part of the readily accessible hardcopy information, we would need to provide the basics for health care and medicine, renewable power generation, and means to advance technologically starting with incredibly primitive tools. We would need to provide all the essential stepping stones, from Bronze Age technology up through Silicon technology, in chapters that were implementable using only what was available for prior technological stages. We also cannot assume fossil fuels, and should not assume any particular climatological or atmospheric conditions (including not being solely reliant on sunlight).
Finally, the materials would need to include the basics of philosophy and mental health care. Tolerance would need to be taught as a fundamental, lest infighting defeat the entire purpose. In any situation where these materials would be needed
Once established, copies of these documents and materials would need to be made in many different languages, and stored in many different locations, to ensure redundancy.
Second, how can the human race survive culturally. This means not only the technical knowledge of the species, but also its cultural history. The reason this is fundamentally different than the preceding issue is that culture will not only always survive on its own whenever people do, but it is always materially changed by any great event that people experience. In other words, some type of culture will still exist, but it will be altered by the process. In any situation where society would need to be rebuilt, the dangers of cultural contamination must be considered to ensure that not only does our cultural heritage and history survive, but that it survives in a way that will not cause the same problems to happen all over again.
The problem with current human culture, pretty much across the board, is that it tends to fracture into opposing and divisive elements. People form groups for protection, but too often that protection takes the form of opposition to anything or anyone different. As noted above, tolerance would need to be taught as a fundamental concept. The idea of their being a One True Way that is opposed to all other alternatives is inherently dangerous, and likely what will be the cause of any species or artificial global disaster. To offset this, the ideas of tolerance and cultural acceptance would need to be inherent and ingrained in anything done to preserve the species. In a sense, to survive culturally, the species as a whole would need to be willing to abandon much of its pre-existing (current) culture -- namely the aspects that cause people to fight amongst themselves merely because of irrelevant differences.
Among this information would need to be the concept of laws. Now, laws in modern times are grossly misunderstood, because people have forgotten the reasons that moral and legal systems split so long ago. There are essentially three types of laws: crimes against people; crimes against property; and crimes against convention/tradition. Crimes against people are those that harm the individual: assault, battery, rape, homicide, kidnapping, fraud, inducing fear (threats), etc. Crimes against property are those which annoy others, but are reparable: theft, vandalism, trespass. Crimes against convention are those where there is no actual harm done, but either a risk of harm is created (DWI, speeding, negligent operations that do not cause actual damage) or there is moral offense given (voluntary prostitution, bigamy, profanity, obscenity, etc). When building a new system of laws, this philosophical difference would need to be inherent in the system. Why? Because tolerance means accepting and tolerating differences in culture. Laws cannot punish based purely on moral codes, absent objective harm, unless we're willing to accept religion-based governing systems. Crimes against property should be repaid under a straight tort theory for damages and restitution (unjust enrichment), unless the criminal has acted so egregiously that no reparation can be made. This keeps the concept of property being less valuable than human life, which is necessary in any effort to preserve the species. Crimes against people need to be punished, but remembering the difference in value and benefit between deterrence, rehabilitation and retributive models. This inherent valuation of personal interests over property rights, and in the promotion of personal freedoms except as required to preserve the common survival is too important to leave to chance.
Third, we have the question of how the species can survive genetically. Let's assume we can preserve the knowledge necessary to rebuild a technologically advanced civilization, and that sufficient cultural data can be preserved both to reflect the global history and the need to not make the same mistakes again.
James P Hogan wrote a book called Voyage from Yesteryear, which explored on technological solution to this problem. There have been others. But the essential concept is that we can't keep all of our eggs in one basket. Earth, as a celestial body, will survive regardless of what we do to it. That doesn't mean the biosphere will survive, nor does it mean that our species will survive on earth. The only option is to spread the species out among the stars, taking care to both preserve our intellectual knowledge and to cure the cultural defects (regarding polarization and bickering) that are likely to be a continuing threat. To that end, any colonization efforts need to be as culturally and politically neutral as possible.
Finally, we turn back to now and look at the future from here, rather than from there. The above answers deal with how to recover the human race assuming it reaches the point of near-extinction. The better solution is to prevent us from reaching that point in the first place.
I've already talked about the way culture and mindset and law would need to be restructured during any rebuilding. That doesn't stop us from taking those steps now to prevent a future conflict.
Tolerance of differences is not just an ideal. It is a necessary survival trait. The greatest threat the human race poses to itself is the idea that only one viewpoint should -- one mindset, one religion, one culture, one nationality, etc. We must let go of this isolationist us-against-the-different psychological taint. We need to start teaching our children now, not just math and science and reading, but tolerance and acceptance and logic and peace. We need to preserve not our own way of life, but our way of living with others. We need to start changing the laws, restructuring the governments, destroying the armaments. We need to stop trying to impose our beliefs on everyone else, stop invading countries because we don't like their government, and stop blowing people up because they are different.
Yes, easier said than done. But violence beget violence, and the methods being used for the past several decades haven't worked to stop further violence. Either we need to go all out, and destroy everyone who can be a threat, or we need to change the focus entirely, and start teaching people how to get along.
Posturing and political threats just give rise to further conflict. Bullying just causes people to think that violence and hatred are the answers. They're not. As a species, for us to survive we all need to learn to think a new way. The efforts described above are a good start to helping us understand what really is important to us and what we truly want to survive into the oncoming centuries. If through that process we manage to avoid the global singularity and avoid destruction, so much the better. But if we don't learn our lessons now, the steps taken to preserve our species and its accumulated knowledge will at least provide for another chance down the road to get it right.
And as long as we can keep trying to make things better, we haven't lost.