The idea is to live healthily on far less sleep than normal. It is based on the theory that the mind performs most of its recuperative tasks in half a dozen short bursts spread out through a normal, monophasic night's sleep. If the brain could be persuaded to do this useful sleep all in a block, we would need to sleep for only an hour and a half!
At least one well-documented experiment has shown that a subject was able to continue for two weeks on this schedule without any reduction in alertness. Indeed, after the initial adaption period, alertness actually increased a little above the baseline established with a monophasic sleep pattern. However, the duration of the experiment was only one month, (including a period of normal sleep calibration at the beginning, adjustment to the schedule, and a study of returning to a normal sleep pattern at the end) so we do not learn much from this experiment about its long-term stability.
Although this is the ultimate target for those who want to spend the absolute minumum time asleep, it poses significant practical difficulties fitting in with other lifestyle constraints. There are often claims that famous historical figures used the Uberman schedule, but little firm evidence is offered. I strongly suspect that in fact these people just used naps effectively to shorten their core sleep. Some professions do use a schedule like this, but the examples cited normally involve exceptional circumstances (such as maintaining a continuous watch on a short-handed ship at sea, or coping with an emergency in a military situation).
The bad news is that it is very difficult to adapt to the system. It takes a tremendous effort to train onseself to use it and to stick to the plan. I thought I had a fair amount of motivation for the project, but it is really hard to get up at 04:00 and find the incentive to do something useful.
The really bad news is that, at least in my experience, the pure system is impossible to sustain. There are some common activities that just do not fit in conveniently with the rigid four-hour cycle. I am fortunate to have an employer who tolerates my working hours being somehwat out-of-phase with others', so work was less of a problem for me than it might be for some---in fact, if anything, I became more punctual as a result of the strict schedule---but normal social activities, such as having a meal and watching a film, don't always fit in to a 4-hour time slot. Although friends would put up with my minor eccentricity of having a short nap in the middle of an evening, that's an awkward thing to ask if you're out with just one person, or with a group you don't know so well. And there is the practical issue of finding somewhere comfortable and quiet enough to nap.
There is some more good news, though. Although I found it impossible to maintain the pure schedule, trying to do it has taught me how to nap effectively. This alone has been worth the effort. I find that if I can have a good half-hour nap at lunchtime I feel much more alert in the afternoon. I usually feel a little bit tired and have another nap when I finish work. With just these two extra naps, my core sleep time is around 4 to 5 hours and I usually wake naturally at the end of this period feeling refreshed. I am still fairly tolerant of disruption to the routine. If I have to miss one lunchtime nap or one evening nap, it doesn't seem to do any harm at all. Conversely, when on the full schedule, I found that I was very fragile: any disruption to the cycle longer than about an hour or so upset me; missing a nap completely was immediately disasterous, setting off headaches and blocking any sleep for hours.
I kept log of the early period of adjusting, but I haven't maintained it recently. I should do, now that I have settled in to what appears to be a long-term routine.
The first thing and most important thing I would advise is that jumping in at the deep end is a recipe for disaster. Most people who have kept blogs seem to try this first and the outcome is always the same: they give up. I did myself.
If you can resist the temptation to do the dramatic, I'd suggest the gentler approach I did the second time. Make yourself take regular naps. One or two a day. Find somewhere quiet you can relax and close your eyes for half an hour. Set an alarm for about 30 to 40 minutes---it's important that this is a short nap or you'll mess up your nightime routine. If you're like me, you'll find that at first you don't sleep at all, then you do manage to doze but the alarm spoils it just as you're getting settled and you're all groggy, then you get used to the timing and you wake up before the alarm feeling clear-headed. It's lovely when that happens.
I tried an evening nap and a lunchtime nap; at first the lunchtime one worked better, even though it was a bit more awkward, but I was soon sleeping a little in both. Don't feel that you have to sleep or that you've failed if you don't sleep---even now I'm well into the routine, I don't always sleep but I know the rest still does me good.
After doing this for just a few days, I started waking up earlier naturally, long before the alarm which normally woke me. My core sleep shortened by about an hour and a half. I've been sticking to this plan now for a couple of weeks and it seems quite stable.
One trap I've fallen in to more than once is to let my core sleep start time slip later. Because I'm so much more alert in the evening, I find I get stuck in to exciting projects, like I used to in college... and then before I know it, dawn is rising. Luckily, with my naps to restore me though the day, and perhaps a bonus late evening nap to catch up, I can get away with this occasionally without any ill-effect, provided I can catch up the next night, but I can't sustain it indefinitely.
After some months, I found that the inconvenience of the lunchtime nap is often too much to bother with, so now I just nap for about 40 minutes when I get home. I'm then ready to have a productive evening until about 02:00 or 03:00 when I start feeling tired and go to bed. I fall sleep immediately and usually wake before the alarm at 07:30. This has lengthened my core sleep a little from what it was when I was doing two naps, but it's still shorter than with no naps. I've been doing this now for more than a year, so I am confident it is a routine I can sustain indefinitely with no difficulty.