The Universe is 73% Dark Energy 23% Dark Matter and 4% Ordinary Matter

We can see galaxies and (with the Hubble telescope) see the speed at which they rotate. We can also calculate how much the stars in those galaxies mass. The problem is, that much matter, spinning at those speeds, would fly apart. Even adding in planets, dust, and black holes, there still isn't enough matter in galaxies to hold them together. Not even nearly enough. There shouldn't even be galaxies anymore, just scattered stars. But there are still galaxies, so something we can't see must hold them together.

The leading contender for that something is matter that doesn't interact with normal matter or energy but does create gravity like normal matter. We call that hypothetical something dark matter, and we're trying to figure out what it is.

From observing the movements of galaxies and the apparent mass they contain, we can approximate how much gravity would hold them together, and that gives us the amount of dark matter.

Dark energy comes from a different observation about the universe. There is a type of supernova called 1A, which is an exploding white dwarf star. Since white dwarfs explode at a certain mass, the explosions are always about the same, and each 1A supernova is pretty much the same brightness and color spectrum as the next.

Since they're the same brightness, we can calculate how far away they are by how faint they appear. Since they're the same color, we can calculate how fast they're moving away from us - the faster a star moves away from us, the redder it appears- we call that its redshift. (Although, regardless of the speed or direction its source is moving, light always moves at the same speed, movement toward us compresses the light's wavelength, making the light appear bluer, while movement away stretches that wavelength, making it appear redder.)

If the universe started all together and then moved apart at a constant rate, then we would expect the redshift - how fast it's moving away - to be the same for nearby galaxies as well as distant ones. But fainter (more distant) 1A supernovae aren't red enough. Since we're seeing those distant ones as they were when the universe was very young, that tells us the universe was expanding at a slower rate back then. And the further back in time we look, the slower expansion was at that time.

So the universe's expansion has been speeding up. But something must be speeding it up. What? Nothing we can detect. Since speeding up as we know it is always caused by energy, we call this undetectable something dark energy.

Calculating how much the expansion has accelerated, and how much energy it would take to do that to all those galaxies, gives us an approximation of the amount of dark energy.