I am very new to sound design, and I'm wanting to make background ambient sounds for a dark-feeling game. How would I go about doing this? Would I use music creation software like FL Studio, or would I record things and slow them down? What tips and tricks should I use for this?
Just FIND sounds. They come from EVERYWHERE. Some are recorded outside, some in staircases, some are found in patches on synthesizers or even generated in FL Studio-like programs.
You should get intimate with time-based FX like reverb and flange, competent with EQ, and experiment with things like pitch-shift, reverse, and time stretch.
Be creative and enthusiastic about it because everything around you can make a sound.
From my point of view, there are often very good results when you use the best of the both worlds = simple audio manipulation + synthesis. In your case ("dark-feeling game" as you mentioned), it might be fun to work with a sound that is usually considered to be very close to actual ambient music. A combination of some dark electronic soundscapes and layered short - almost percussive - sounds with a reverb that can be even exaggerated. This is just one of many possible approaches, of course. First of all, I would recommend to learn how to manipulate, edit and process simple audio recordings. I'm not very familiar with FL Studio (I remember Fruity Loops), but the freeware solution for learning how to work with samples can be simple as Audacity. If you use FL Studio, I'm sure, you can import edited samples later. At some point, it may be necessary to have a real DAW (you can try Cockos Reaper or MuLab which are cheap when you decide to buy them later, also Logic is very powerful and not so expensive, or you can consider Cubase, Pro Tools etc.). A hand-recorder is always, well, handy when it comes to get original sounding audio samples that can be used later on. Some sort of (software) synth is the another step. My favorite for such purpose is Alchemy from Camel Audio. You can load your sounds into it, apply - for example - some granular synthesis etc and blend it with another one. As you mentioned, tuning sounds can be useful and sometime you can get unexpected scary sounding results, of course. (Find some old guitar, experiment with tunings, record a single chord, slow it down and be creative later during editing/processing!) It's up to you and your fantasy. And don't forget that less can be sometimes more scary...(Limbo!)
There are probably as many approaches to this as there are people doing sound design, there's no hard and fast rules, and finding your way is part of the 'art' of it, the thing that makes it yours rather than someone else's recipe, or worse, a cliche.
First thing to do is get comfortable in some audio editing or sequencing software package. It doesnt which one it is as long as you're comfortable working with it, and it does the kind of things you want.
How do you know what things you might want to do with it? Well, up-front, you wont. It takes time and experience to find 'your' way of doing things, so just experiment until you start to get a feel for it. That might, along the way, entail changing the tools you use, but that's fine.
Dont worry too much about going straight for the specific sounds in your question. Get used to what the software can do; how you can chop sounds up, layer them, alter how they sound, how they play back, and the character that individual kinds of effects processors have when they alter sounds. As you do so, hopefully some of these processes will resonate with you in producing the kinds of sounds you're talking about, your way.
At the same time, think about the sources of your sounds; original real-world sound recordings often have sets of qualities that are hard to replicate in synthesisers, and vice versa. Sometimes you might want something more artificial, sometimes you might want something more organic, sometimes you want realism, sometimes you want the abstract, the alien; sometimes the transformation of something familiar is more unsettling than something comletely abstract.
You'll get further if you focus on the specifics of what you want to achieve, and why, than the mechanism for getting there. Almost any set of audio processing tricks 'can' get you some sort of passable sounds (high pass it, drop it two octaves, drench it in a long 100% wet reverb tada) but once you've built a framework in your head for how these processes fit together, and what to expect of sounds when you transform them in particular ways, you'll be much better off.
There's two large parts to this. Creating the actual sounds and implementing them in game. How you do each will effect the other.
On the very high level, you can use what ever DAW you're comfortable with to create sounds. The setting of the game will drive what sort of sounds you'll want to be creating.
On the implementing side, are you using middleware? What engine is the game using?
Remember the goal is to create something interactive and not static. You'll need to build up different layers and not just one giant loop.
Watch Asian horror films. They are well-practiced at generating suspense with music and sound effects. Mostly it's minor key and discordant stuff. The sound designers who work on thrillers/suspense films use the same techniques such as filters, reverb, and pitch/time shifting that mentioned above to achieve a certain atmosphere. The kinds of sounds people find unsettling are pretty consistent, in my experience. One example is this: if in the game the player turns a corner and sees something creepy run past up ahead, a quick little discordant piano riff would unnerve the player. Add a little compression and EQ and the piano riff will go right up the person's spine.