Before constructing the answer, it's usually good to clarify the problem. First, it's probably good to re-frame it in terms of past and present, not the (unknown) future. For example, assuming there were an extinct civilization 100,000 years ago which managed to pass that one sentence on, what bit of wisdom to the ancient Greeks/Babylonians/Etruscans/... would you expect to be most useful? How and why? What does it mean to be useful, anyway? Useful to whom? To them? To us?

Did they come up with that bit of wisdom by themselves and rejected or ignored it, anyway? Would it have been different if it was unearthed as a relic of a past civilization?

Even though innovation, trade and competition in labor, product and capital markets can sometimes harm individual businesses and workers, restricting these forces almost always reduces the total prosperity of a society.

As far as major scientific facts go, I am surprised that evolution has yet to be mentioned. Let me try:

"All the complexity of Life on Earth comes from a single origin by the following process: organisms carry the plan to reproduce and make copies of themselves, this plan changes slightly and randomly over time, and the modified plans which lead to better survival and reproduction tend to outcompete the others and to become dominant."

In general, I'd expect sentences that convey information about the scientific process to be much superior to sentences that contain merely some clever concoction of facts. Analogous to teaching a man to fish versus just giving him some fish he would have caught anyways given the right method. The only exception would be information that is extremely unlikely to be experimentally discovered* (yet the previous generation stumbled upon) but the expected value of which would outweigh some optimization of the scientific method. (*Before a cataclysm)

Come to think of it, the most such important piece of information (and also keeping with the hypothetical) would be information about the cataclysm (only applies for anthropogenic cataclysms). The reason is that ceteris paribus, a similar pattern (which we would even help along with our usual sentences) could well lead to a similar outcome (another catacylsm). Gotta break the circle.

Alternatively, what about "ALL THESE WORLDS ARE YOURS EXCEPT EUROPA ATTEMPT NO LANDING THERE". Imparts some important cultural information. Hope the poor blokes don't take it too literal and implement a naval embargo of Europe.

If they can understand English, perhaps they can understand math, the supposedly universal language. With that in mind, here is a single equation by Sean Carrol that completely describes the fundamental physics of what he calls "everyday life on Earth".

I'd be thinking along the lines of "keep heating different rocks up a lot, you'll eventually get really useful stuff for building things out."

This is assuming we get fire pretty easily (so we don't have to transmit that knowledge) but reflecting the millenia before our tech included metal.

Wow, I'm missing the more important surplus: "find the plants you can eat and figure out how to grow them yourself in one place."

I'm not enough of a prehistorian to know which came first: metal or agriculture. My principle in choosing one of the... (read more)

Never attribute to malice what can be explained by stupidity.

If I recall correctly, it was only when chemists started noticing that the outputs of chemical reactions tended to factorize a certain way, which is to say that it took millennia after Democritus to get the point where the atomic hypothesis started making clearly relevant experimental predictions.

IIRC, even then, plenty of people considered it somewhat speculative, and it didn't become universally accepted until Einstein's explanation of Brownian motion.

An intuitive, one sentence explanation of the scientific method. Come to think of it this might be handy in general. Eliezer's is already pretty good.

I wondered what Feynman was thinking, so I looked up the context. Here is an excerpt and a longer .doc. Google books. But it didn't help.

Can I use Rule 110 as an extensional definition pointing to what is arguably the central insight of computation? "Rigorously analyze the relationship between the consequential patterns and initial conditions if, for each row of black and white stones, the next row is arranged such that a black stone is placed beneath a white stone if the stone to the right of the white stone is black, a white stone is placed beneath a black stone if the stones to either side of the black stone are also black, and a stone of the same color is placed beneath the stone in the preceding row otherwise."

"Stop trying to sound wise and come up with theories that make precise predictions about things you can measure in numbers."

It seems a bit anthropocentric to assume that the next gang of creatures will also be interested in "sounding wise". Edit: Unless they're humans, of course.

"The new basic principle is that in order to learn to avoid making mistakes we must learn from our mistakes." – Karl Popper, In Search of a Better World.

"It is an attitude which does not lightly give up hope that by such means as argument and careful observation, people may reach some kind of agreement on many problems of importance; and that, even where their demands and their interests clash, it is often possible to argue about the various demands and proposals, and to reach – perhaps by arbitration – a compromise which, because of its eq... (read more)

In my discipline? I guess

Write code that's easy to update without breaking dependent code.

That'll save the ancient programmers of the 1950's some time.

If I were trying to build up programming from scratch, it'd get pretty hairy.

Build a machine that, when "x = 1.1; while (10. - x*x > .0001) x = x - ((x * x - 10.) / (10.*x)); display x" is entered into it, displays a value close to the ratio of the longest side of a right triangle to another side expressed as the sum of 0 or 1 times the lengths of successive bisections.

Math:

"Write down numbers by using ten symbols called digits for the numbers zero through nine, and writing XY, where X is a number and Y a digit, for the number equal to ten times the number represented by X, plus the number represented by Y."

Maybe this could be optimized by picking a better base to work in (2? 8? 12?), but if post-apocalyptic humans have the same number of fingers, then base 10 has its advantages as well.

I suppose something like:

Competition and creation, the former stopping the insane forms of the latter, are responsible for pretty much everything you see, and, if you foster them in your society, can - eventually - give you more than you can possibly imagine.

How many semicolons are we permitted?

More seriously:

"Study processes whose inputs are also their outputs."

"You are not special. You are not a beautiful or unique snowflake. You're the same decaying organic matter as everything else. " -http://www.imdb.com/title/tt0137523/quotes

(Not actually)

Prosperity depends on trust, especially trust that the fruits of one's labour won't be arbitrarily taken away; therefore there should be clear and reliable property rights.