If on a water covered planet, an aquatic species such as the merfolk evolved sapience and now wishes to go into space, how would their spaceship take into account the lack of land? How would a space ship built underwater be able to get into space?
My question differs from this one in that I am asking about how the ship would take off and not at all about suits or design.
When we were first getting into space, we started with very fast, high-flying aircraft. Look at the X series of rocket-powered aircraft used by NASA to test all sorts of things related to space travel. For us, it was a logical step to first be able to get into the air, and then get into space from there.
For an underwater species, there would be a third step. Their first phase would be to get out of the water. Once they had the technology to be able to handle working out of their natural habitat, they would have to figure out how to get into the air. THEN would come the leap to space.
Given that, it seems logical that the best place to launch a spacecraft for them would be a large floating platform near the equator. The platform would give them access to the air, so any space ship would not have to deal with water, air, AND space, but only two of the three mediums. The equator is good because of the bulge of the planet and our rotation, on earth, it gives a significant fuel savings to launch as close to the equator as possible.
Rockets are not implausible. In fact, it seems possible that they might develop rockets before they ever worked out advanced aerodynamic theory. This is because you can create a very simple, primitive rocket by using water trapped in a container that can be heated, forced to expand, and provide thrust. If the species had a reliable source of portable heat, they may have developed the basic principles of the rocket engine long before even being able to build a platform on the surface of the ocean.
Water based species have plenty of access to hydrogen if they can generate electricity (separate it out of the water). That is a staple of rocket fuel for us. This all seems to point toward a space program that runs in parallel with our own, at least in general.
I am not convinced that they would necessarily put the pieces together the same way though. We had hundreds of years of experimentation with ballistics and aerodynamics (mostly for warfare) under our belt before the invention of the rocket motor. We had a darn good reason to try to develop flying bombs that could self-propel and drop on our enemies many miles away. The military incentive to develop rockets was critical to the entire space effort, from the "buzzbombs" of WWII to the ICBMs that provided the foundational technology for the lunar launch. An aquatic species would have a long history of under water warfare, but apart from using the surface to scout or spy on their enemies, what experience would they have with trying to lob missiles through the air? Why even develop artillery on the surface if your enemy's base of operations is the bottom of the ocean?
Necessity is the mother of invention, which means that I bet these guys would be considerably MORE advanced than we were before they actually put all the pieces at their disposal together and built a rocket capable of putting them into orbit. (Remember the motives for us to be in space even now: spying on enemies ON LAND -satellites aren't very good at seeing anything on the bottom of the ocean, which is what they are most concerned about). Ironically, they might develop this kind of technology as a reverse to our own nuclear subs. We keep submarines full of ICBMs under the water because it makes them easy to hide, so we know that no enemy can possibly take out all of them at once. Maybe they want to get into orbit (or the air) for the same reason? Hide their nukes from their opposing nations because nobody pays any attention to whatever is flying around in the sky or orbit.
Believe it or not, we land-folk have already done something similar!
The Trident-II Ballistic Missile (and its ilk) are designed to be launched from a submerged Ballistic Missile Submarine like the Ohio-class or Typhoon-Class. Obviously this is not a rocket intended for orbit, but the principles would be largely the same in either case: accelerate the vehicle until it breaches the surface of the water, then ignite the rocket motors.
There are a number of possible ways to accomplish this. From near the surface of the sea the rocket could be pushed using a pressurized tank, much like the Trident does. From the ocean floor it could be accelerated using more traditional motors, driving water jets of some sort. Even some sort of magnetic acceleration might be possible.
If I were designing the launch system, I would build a launch platform on a high "peak" near the surface and launch the rocket using pressurized gas or water. The rocket accelerates upward, breaches the surface, and then ignited the engines and off it goes.
Any water covered planet would have an atmosphere, even if it is made only of water vapour. That's because if you start with an ocean interfacing with outer space, the pressure different will cause water to boil and evaporate.
So the best course for your merfolk is building a floating launching station and launch from there. That's because since atmospheric drag should be significantly lower than water drag, launching from air would be cheaper in fuel.
Alternatively, a flying vessel could take off from the sea and gain altitude continuously until it reaches space, where it could then accelerate further to establish an orbital path. I don't think this is as efficient as launching a rocket from a floating platform, but then my experience with this method is limited to Kerbal Space Program. I am not a true rocket scientist.
Depending on the craft shape they could use an underwater launch system. There is a system that in theory can shoot supplies into space and the cannon is mostly underwater.
Basically a long barrel (submerged underwater except for the end) is used to fire the spacecraft, like a gun, into space. This type of system would not require land and could be modified to launch various sized/shaped spacecraft.
So, the other answers make some very good points, though the Trident-II Ballistic Missile isn't a great starting point just as a surface-to-air missile is much easier that a surface-to-orbit rocket. Part of this is due to the stress of breaking from gravity with heavier objects. A missile's payload is significantly smaller than a rocket that is carrying beings and their sustenance (at a minimum).
Additionally, though you specify that it's not about suits and design, it makes sense that at a minimum, a substantial amount of water would need to be on the craft for waterborne species to survive, and water is heavy (much heavier than air), increasing power requirements for liftoff and reaching sustainable orbit.
Lastly, I agree that having some platform to launch from is nearly imperative as, just like water is heavier than air, water resistance is greater than air resistance, and the force required to launch from even a few hundred feet below surface would be considerably great than from the surface. Especially since, ostensibly, it would be adding a third stage (water-to-surface, surface-to-air, air-to-orbit), meaning more weight and more friction through the water.
It's not impossible, but launching from the bottom of the sea would be extremely difficult.
Would it be at all possible for the merfolks to build a giant electromagnet and launch using a similar albeit smaller electromagnet of an opposing polarity to the second, apply enough energy and the ability to launch seems feasible in my head. I am not a scientist though by any means and do not know if this could legitimately work, but for a sealocked lifeform this also seems better than trying to light a fire underwater.