Guide to telescience
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Welcome to Telescience, the room where you teleport things/people/bombs you aren't supposed to have into places said things/people/bombs aren't supposed to be, or use it for legitimate purposes.
Please note that the Telescience Lab was removed from the map we run at /tg/station 13. If you want to do telescience, you'll first have to build the equipment yourself with components from Research and Development.
Tha' Hell is This New Fangled Telescience Stuff That Runs on That ElectricialTricity?
Telescience is a single room at the south end of the Research department hallway.
This area focuses on teleportation, both sending and receiving. It is equipped with a Telepad, a secure room to teleport people and things in and out of, and several handheld GPS readers.
Telescience is imprecise, but potentially extremely useful. Try teleporting GPSs to see where they go, and then from there you can move objects or people back and forth from your lab. Like all science rooms, experimentation is key!
Holy Shit, I Will be the Ruler of Space and Time!
A word of warning. Telescience requires math. Of course, as a scientist, you have a good understanding of mathematical knowledge and projectile trajectory, right?
The telepad console has 4 variables that can be set:
 Bearing (measured in degrees, can have a value from 0 to 360)
 Elevation (measured in degrees, can have a value from 0 to 90)
 Power (measured in integer units, can have a value from 5 to 100 provided you have enough Bluespace Crystals on hand, power levels from 5 to 25 are available by default)
 Sector (defines the zlevel which will be teleported to/from, default is 1, corresponding to the main station zlevel).
Together, these 4 settings define the coordinates whatever or whoever is on the telepad will find themselves after you push the Send button on the console via the following equation:
 (destination X, destination Y) = (telepad X + distance * sin(bearing)),(telepad Y + distance * cos(bearing))
where
 distance = (2*(power*sin(elevation)/10)*(power*cos(elevation)) = (power^2)*sin(2*elevation)/10
In dummytalk, Bearing specifies a direction from the telepad (with 0 being North, 90  East, 180  South and 270  West) and Elevation and Power specify how far from the telepad the target will travel.
How to Rip a Hole in the Fabric of Space and Time Itself to Perform Useful Duties
First things first, the telepad needs to be linked to the Telepad Control Console. To do this you'll need a screwdriver and a multitool. Use the screwdriver on the telepad to remove the maintenance hatch, then use the multitool on the telepad to save it's linking data into the multitool buffer. Screw the maintenance hatch back in and then upload the telepad data to the control console by using the multitool on it.
At round start, the telepad will be calibrated. That means the following: the Bearing setting will be offset to a random value between 10 and 10 degrees, and the Power setting will be offset randomly from 4 to 0. At this point, there are somewhere between 30 and 40 uses before it will have to be recalibrated. Every time the crystals are recalibrated, the remaining uses until calibration is needed again will be a random number between 30 and 40. When recalibrating, the bearing and power offsets will be rerolled. These values do not stack, so they will always be within these ranges. To find out these offsets, you will need those little gizmos called GPS. The round starts with a number of them on the table in the Telescience Lab. Grab two, place one on the telepad and the other in your pocket.

Now this next part requires some math and a calculator supporting square roots and inverse trigonometric functions, specifically asin() and atan(). If you're incapable of math, ask yourself what the hell are you doing in the Research Division of the most hightech space station ever built, and apply to Head of Personnel for the Clown's job.
First, let's find the power offset. It is most simply done by setting elevation to 45. Elevation set to 45 sets the sin(2*elevation) to 1 so the equation for the distance simplifies to (power^2)/10. For example if you teleport something with power 20, it should be (20^2)/10 = 40 tiles away. That's where the power offset comes in, as the GPS will actually be in ((poweroffset)^2)/10, so, using the previous example and if the offset is, say, 4, the GPS will be actually ((204)^2)/10 = (16^2)/10 = 25.6 (rounded to 26) tiles away. So, to find out the power offset, you need to teleport the GPS with 45 elevation and see how far away it actually flies. Let's designate the GPS coordinates as X and Y, and the telepad coordinates as Xt and Yt. Then the formula for the distance from the telepad to the GPS is:
 distance = sqrt((Xt  X)^2 + (Yt  Y)^2)
and the equation for actually finding the offset is:
 ((poweroffset)^2)/10 = distance, therefore (poweroffset)^2 = distance*10, therefore poweroffset = sqrt(distance*10).
So, to recollect, to find the power offset you need to:
 Teleport the GPS with settings 0 bearing, 45 elevation, 20 power.
 Using another GPS find out how far did it go in both x and y directions (say, it travelled X tiles on x axis and Y on y axis).
 Calculate the distance from the telepad to the GPS as sqrt(X^2 + Y^2)
 Multiply it by 10 and extract sqare root.
 What you see at your calc now is power minus offset. As the power was set to 20, to find offset, you need to substract the number you've got from 20. So, for example, if you got roughly 17, the offset is 3 (remember it can be only integer).

Now, to find the bearing offset. When you teleported the GPS, you might've noticed it didn't go precisely north, although the bearing was set to 0. The bearing offset is to blame. Once again, assume the GPS travelled X tiles west and Y tiles north. Then, by dividing X by Y, you get the tangent of the offset angle, and the angle itself can be calculated as offset = atan(X/Y) after that, you need to convert it from radian to degrees so it is better to do it like this offset = atan(X/Y) * 180/pi (it's also integer, so feel free to round). Given the GPS travelled west, that will be a positive offset that will be added to your bearing, so you have to compensate by substracting it from the bearing you will be setting. Inversly, if the GPS has gone east, the offset is negative and you need to add it to the bearing.
Congratulations! Now that you know both offsets, you can teleport anything with some deadly precision or steal some highsecure items in the most stealthy fashion without having anyone see the GPS tools dancing around! So, how do you put that knowledge to use? Let's assume you want to teleport something X tiles west and Y tiles north. First, you again need to find the distance as sqrt(X^2 + Y^2) (let's designate it D). Now, set the power setting so that ((poweroffset)^2)/10 (let's designate that number as Dmax) was greater than your distance. (If you can't, you need to find you more bluespace crystals). Now, once the power is set, you need to adjust the elevation. Divide D by Dmax. As Dmax is greater, you'll get a number less than 1. You need to calculate the inverse sine from that number and then divide it by 2. In one formula,
 elevation = (asin(D/Dmax))/2.
Now the bearing setting is obviously dependant not only on the distances the object has to travel along the X and Y axes, but on the general direction it travels to or from (northeast, southeast, southwest, northwest). To set the bearing, you'll need to calculate atan(X/Y) if the destination is northeast or southwest, and atan(Y/X) otherwise. Both X and Y numbers here have to be positive (just the distances on X and Y axes without signs). (Writer's note: wish I could add a picture of trigonometric circle in here, that would explain everything much better than I can in words). You'll get a number between 0 and 90, which will be your bearing plus(or minus) offset if you're sending northeast. To send something along the same distances on X and Y, but in the other direction, you'll need to add a multiple of 90 degrees to it. So:
 To send north and east, don't add anything.
 To send south and east, add 90.
 To send south and west, add 180.
 To send north and west, add 270.
Now compensate for the bearing offset, punch those numbers in the computer and hit that Send (or Recieve) button! If you're not miscalculated and everything was done right, you should now have DAT FUKKEN DISK on the telepad or a maximumyield bomb at the AI core. Enjoy your nearomnipotence, you've truly deserved it.

Sadly, every 30 to 40 teleportations (roughly) the Telepad will fizzle. This means you need to click Recalibrate and start from step 1. Learn to recalibrate quickly, or you may end up in a heap of trouble.
Leave handy beacons around the station, and GPS units at interesting locations in space, and you can easily find them again. It's worth putting something down in the Medbay so you can quickly send the wounded and the dead there.
Also, note that the maximum radius you can reach is proportional to power squared, so, with so much as three or four extra crystals, your reach extends immensely. Just insert them into the console and higher power will become available. This also amplifies the recharge time between teleports and the energy the telepad consumes from the room's APC.
Challenges for the Robust in All of Us
 Be useful and teleport dead bodies to Genetics for cloning, or injured crew straight to Medbay for treatment!
 Teleport an Engineering Cyborg straight to a hull breach!
 Borrow all the Chef's donuts!
 Teleport the last remaining revhead into the Brig for implanting!
 Find the remaining Bananium ore and construct a H.O.N.K. mech for the Clown!
 Teleport the Nuclear Device around during a Nuclear Operatives round! Bonus points if it's right after they stick in DAT FUKKEN DISK and before they input the code! Double bonus points for teleporting it to the derelict!
 Teleport a bomb onto a malfunctioning AI's core!
 Teleport the WGW reader into LORD SINGULOTH!
TL;DR
If you're not a real scientist who likes to do science and learn from it, you can use these:
 Coordinate maps:
 Zlevel 1 (station itself): boxstation, metastation
 Zlevel 3 (old telecommunications sat): tcommsat, abandoned teleporter, white shuttle
 Zlevel 4 (derelict): derelict, derelict teleporter, clown shuttle, DJ station
 Zlevel 5 (mining): main outpost, west outpost, north outpost, labor camp, alienweedcovered part
 Coordinate Maps AllInOne zippackage
Traitorous Uses of Telescience
 Build a crew monitoring console. Build r windows around the telepad. Enter the cords of your target/whoever the fuck you wish to kill, teleport them in, laugh at their confusion, then send them to deep space. Laugh once more. Repeat.
 Also teleport in Guns from the armory. Teleport in your theft objectives.
 Teleport in the clown, remove his headset, and close the blast door. Congrats, you have your very own pet just like the HoP!
 Also teleport in Guns from the armory. Teleport in your theft objectives.