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This tutorial will show you how to get Science, and with this knowledge you'll plan missions better and build your craft to maximize the results of picking up stuff and looking at things in strange new places.
The current technology tree takes over 16000 Science Points to unlock completely, so it is fairly important to efficiently gather as much as possible of the Science that is available.
For Beginners: what is Science, anyway?
Science is making observations in new places with your crew and scientific instruments, then getting that data home. Too abstract? Then let's try a short tutorial: design the simplest ship possible, a plain Mk1 Command Pod and nothing else. Hit "Launch". Of course, that pod won't go anywhere, but it doesn't need to. On the launchpad, right-click the pod, select "Crew Report", and you're doing science! You cannot transmit the results, because your simple craft has no antenna. In order to get the data home, you need to recover your vessel.
Important Science Fact: whatever you do in the field, you won't get any Science Points until you return the results, either by radio transmission or by recovering the vessel (or Kerbal) where the results are kept.
A Crew Report is just one Science Activity; your crew may also leave the pod and create an EVA Report or perhaps collect Soil Samples. There are also dedicated science instruments such as thermometers or the Mystery Goo™ Containment Unit.
If you paid attention during the brief tutorial above, you noticed that you got a "Crew Report from the LaunchPad." The Launch Pad is considered a "Biome." That is, a special location where you can collect Science. Just getting your capsule off the pad (generally by launching it) will move it into a new biome where you can get a new report for fresh Science Points. Actually, Kerbal Space Center alone is made up of 33 different biomes; the rest of the planet is not as finely detailed, but Mountains, Deserts, Icecaps and so on are easy to make out from above. Badlands also exist, but are much harder to find (since they are mostly on the other side of the planet).
At the Space Center, many of the buildings have a small biome around them, such as the Administration Facility. Many individual structures also count as special "biomes" in themselves, such as the VAB Main Building - and these biomes can only be accessed by touching the building with your craft. (That is, running into one at very low speed and setting the brakes.)
So, getting Science all comes down to traveling around in a craft that has a lot of scientific instruments on it, visiting as many biomes as possible, and gathering all possible forms of data at each of them.
On Mun and Minmus every large crater (or depression, respectively) is a biome of its own, plus a few more in-between. The latter are nowhere near as obvious as desert and grassland are on Kerbin, but there are slight differences in the look of the surface. For more detailed maps, refer to the Biomes article. The same is basically true for all the other celestial objects.
The Importance of Scientists
Several types of instruments (ie. Goo and Science Jr.) can only collect data once - unless a Scientist resets them during an EVA. If you are taking a long journey (to another planet maybe?), and wish to collect many samples, then your choice is to either bring a Scientist along to reset the units, or to have a tremendous number of devices. This applies to short journeys, too. Landing is dangerous, and you will want to minimize the number of times you need to do it - by collecting as much Science as possible, with as small a craft as is convenient, each time.
Also, Scientists have the ability to activate a device (to collect new data) during an EVA. This can be useful in cutting down the number of EVAs needed to download data from the instruments - and can be especially useful to easily get a "landed" status in a water biome (see below).
A "Science Activity" means using either a crew member or a scientific device to gather new data. There are 4 crew activities: Crew Report, EVA Report, Surface Sample, and Asteroid Sample. There are currently 7 scientific instruments.
A "situation" or "status" is the current condition of the craft or Kerbal: landed, splashed down, flying, etc.
As stated in the Science article, you can collect new Science from every legal combination of biome, situation, and activity - but the devices have many limitations on what is "legal." See this chart.
When you are starting, this means that for each of the 9 natural Kerbin biomes you want to get a status of both "landed" and "splashed down," to double your opportunities to get Science. Which means that you need to find water in the Badlands, Desert, Grasslands, Highlands, Ice Caps, Mountains, and Tundra. And you need to figure out a way to land on top of the water without being "splashed down".
Kraken Warning: as of version 1.0.5 - swimming in the water, taking a water sample, then attempting to reboard your floating craft may cause your craft to explode. Creating a prior quicksave, then reloading it may cause your craft to explode again after a few seconds.
Getting Results Back Home
As said above: doing lots of science in the field will not suffice. Only when the results somehow find their way to your R&D department will you be credited with science points.
Transmission and Recovery Values
For every result, you have the choice to either transmit the data or to keep it. For most experiments, transmission will yield significantly fewer points than recovering the results - so much should be obvious. The two bars at the bottom of that window carry a lot of information, though:
First example, Mystery Goo: The absolute length of the bars represents the total amount of Science Points that can be collected from that particular experiment, in this case that would be 13 points. The bright green line shows the fraction of points you will get for performing the experiment once; in this case, 10/13th or approx 77%. If you repeat that experiment, you will get 77% of the remaining three points, and so on. Every time you repeat that particular experiment and recover the data, you will receive ~77% of however many (or few) science points are still left. As a rule of thumb, repeatable experiments are pretty much depleted after the third time.
The blue bar indicating transmission value follows a similar pattern, but please notice how even the dark blue stops far short of the total amount. No matter how many transmissions you make, you won't receive more than 30% of the available points. Once you are above the 30% threshold (eg, because you already returned one container), further transmissions will be worthless. The Mobile Processing Lab MPL-LG-2 can boost that number a little (more on that below), but the fact remains: transmissions alone will get you only so far.
For comparison, an EVA Report: Whether you transmit or return the data, you will get the full science points all in one go. That kind is often called a "non-repeatable experiment", although "no need to repeat" would be more precise. You may of course repeat it; filing the results more than once won't get you any more Science Points, though.
Recovering the results while leaving the equipment: Taking and Storing Data
All results are kept somewhere. If your Kerbal takes a surface sample, he carries it on himself at first. The moment he enters a pod or capsule, the result is transferred from Kerbal to capsule. A message on the screen notifies you of this, though it fades pretty quickly.
If your research is based on equipment, like thermometers or the Mystery Goo™ Containment Unit, the results are stored on said equipment. Probably the most convenient means of recovering these results is to just recover the science modules, but this is not the only way: a Kerbal can download the data (right-click during EVA, while in close proximity to the equipment in question) and subsequently transfer it to a pod, capsule, or some other module. Simple experiments (e.g., thermometers) will then be available for immediate re-use; more complicated ones (e.g., Mystery Goo) will need to be "restored" by a Scientist. Once the data has been downloaded from them, spent modules may safely be left behind.
Getting and staying close enough to download data can be a hassle sometimes, even on the ground, much more so in space. Having ladders to cling to makes this much easier.
Kerbals can also take data from one pod and move it to another: that's important when you want to make an Apollo-Style Mission where the Lander Module and the Return Vessel are two distinct spacecraft. To do this, the kerbonaut must EVA, move close to one pod, take all the data from it, move to the other pod, and store the data onto the new pod or board it.
Most modules have only a limited capacity; typically, command pods can only take "one of each": one surface sample from here and one from there is possible, but if you want to take home two surface samples from the same site you need to bring two pods. Incidentally, it is not necessary to board a capsule only to transfer the data, you can again do this by right-click while being close to it. Putting data onto a module from the outside (i.e. without boarding the module) will store only as much data as the module can take, the remainder stays with the Kerbal.
On an EVA, Kerbals may only perform each crew activity once, until that data has been stored in a module. However, Kerbals are able to temporarily download an infinite amount of data from instruments and pods -- including storing multiple copies of identical data. But eventually the Kerbal will probably need to board a pod, and pods usually have much stricter limits (as said above).
If you transmit data, you will implicitly "take" it from a module without the hassles of EVA. The other effects regarding re-usability and the possible need to restore the module are the same, regardless of whether you take the data manually or by transmission.
Mobile Processing Lab MPL-LG-2
The Mobile Processing Lab MPL-LG-2 improves the value of science data before transmitting it; it has no effect on data kept aboard. Crew Reports and EVA Reports have no penalty on transmitting them, so lab processing doesn't benefit these two. The others typically improve by 50% (if the standard Transmit Value for a given experiment is 20%, the Lab pushes this to 30% and so on). While quite a boost, this still leaves a lot of unrecovered Science Points, so you probably still want to bring data back home.
For others, it can squeeze out points from reports that at first have "+0.0 Science" value to transmit.
However, the Mobile Processing Lab MPL-LG-2 can also store infinite amounts of scientific data - even multiple copies from the same experiment in the same situation & biome.
Both cleaning and processing required a certain amount of time and electric charge. Cleaning an experiment requires the same amount of energy as processing its report data.The Mobile Processing Lab MPL-LG-2 can also store multiple copies of scientific data - even those from the same experiment in the same situation & biome. For example, a lander could conduct three material studies with separate SC-9001 Science Jr. units, rendezvous and dock with a ship containing a Mobile Processing Lab MPL-LG-2, then have a Kerbal on EVA "Take Data" from each SC-9001 Science Jr. and place it in the lab. This must be done once per piece of data, as a Kerbal can only store one type of unique data at a time. Most experiments can be 'maxed out' in a single trip by recovering three or four samples.
Refer to the main article for ramifications and usage scenarios.