Note: This is for people who for any reason don't have the budget to hire a sound designer. This is not a tutorial on how to compose, are quick tricks so your starter game or prototype isn't soulless for lack of music. (Edited by mod at OP's request)
I think the biggest fear of every solo or small team developer is the music, think that they can learn to code, to concept, even to 3D model but NEVER compose. The thought of learning music scares them to death, they think that its just not for them and if playing and instrument it's hard, composing it's an impossible situation, but there is a problem with that thought...
You're a creative person, and you love music
Music is inside all of us, I literally can't think of anyone who doesn't love music, its just in our nature.
So if music is our nature, how hard can it be to create music?
Not that hard, actually. I'm sure in some moment of your life you have singed something instead of talking it, or scatted some extra punch line to a song of your liking, or just whistled something that you never heard but came out of you because you were in a good mood, or anything related to creating a melody with your mouth.
The problem its not creating the music, its writing it and develop it...
You're better composing than you think
Probably you have been in the thought that music it's too complicated, and when you see a music sheet it's just way too much, and involves a lot of knowledge and years of practice.
At the most part you're right, music is no easy skillset and usually comes with mastering a lot of different instruments in order to understand them, but to create environment music you only need a few handful of that skills. And when I say just a few I'm no kidding, really you just need to know what you want and then follow a small set of rules while following your heart.
I know you don't believe me, so I will prove with this small video. You will "compose" with only 6 notes (download a piano app first, if you have a keyboard even better):
I know the video says hollywood music, but it easily applies to videogame music as you may see. And if you watched the entire video and experimented with the information you're probably a lot more confident about your music skills and thinking "how many of this tricks there are?"
A LOT
Which leads me to my next point:
You don't want to be a musician
Or maybe you want to personally, but at least for environment music you don't need to be one.
Environment music is fairly simple
Seriously, saying that to make a nice loop (because environment music is no more than that) is being a musician is an offense to all the real musicians in the world. A musical piece is a small story, and as any story it has a narrative, an individuality, usually needs to be catchy and a lot of other factors that are the true challenge of composing.
Instruments are just a plus
Also, you don't need to learn no instrument. It would help, for sure; it helps you to understand better why music happens, gives you a natural physical way to express your music, etc... but probably you already are full of tasks and don't have time to develop fine motor skills. So don't think that you can't compose if you can't play an instrument; musician often say that if you can't play you are not really a musician... but as I said: you don't want to be a musician.
You don't need music theory
Ok... maybe I'm exagerating with this one. But as you saw in the video, you can compose just following a small sets of rules, and depending on how complicated you want you music for your game is how much you will need to expand and understand that rules.
You only need the right tools
As game developer you know that all the tasks you perform would be a looot harder and slower without your favorite tools (game engine, graphics software, etc); this tools not only save us a lot of time, we don't have to even understand how they work , only use them to create and manipulate our idea.
Take GameMaker for example, you don't need to know coding to produce an entire game. Sure, it will limit you to something simple, but you're indie, you know: Simple can be better.
So it's clear that there must be a tool that eases that process. So, what tools you need?
As always, the answer is: it depends on what you want. But for now, for you to understand how this tools usually work and what you need to search for, I'll give you this one:
Learning Music - Ableton
Its a free web tool where you will learn to compose in a different way than the usual used in music schools. First you will learn to compose with nowadays technology, and then you will learn the theory of how you did that. Sounds weird, right?
Not that much actually... when we learn to talk first we learn to produce sounds, then words, then speak, then read, then write, and only then we learn the rules of everything we have learned. So it's pretty much the same course, only using music as our form of speech; because, at the end of the day, thats what we're trying to do: communicate with sounds what we communicate with our graphics and our mechanics and every part of the gameplay.
Start now, and keep practicing
As any other skill, composing, even small simple loops is no easy task. It's not as hard and as time consuming as you think, but it surely is a challenge.
So if you're developing your own game and you don't have the budget for a sound designer or even you don't think anyone can express what is really on your mind, or any other reason you think you need to produce your own music, I really recomend you to start right know with the Ableton tool and give it just a few minutes a day with a little "composing" practice (really, you will be experimenting day 1) and keep experimenting there until you think you have enough to migrate to a real DAW and maybe keep learning for you to create more kick-ass pieces.
So I said: music it's our nature, you're a creative person, environment music is a lot simpler, and there are tools that eases a big part of the process, and for all that I really think that you can write your own environment music if you want.
I hope this helps you to understand a little better music, and specially overcome that thought that music its not for you, because music is IN you.