Do Need: to Make Music Directly
The most important factor in composing music is musical intuition. And the only way to develop intuition is to make music by your own actions with an immediate result. In other words, you can sing, you can hum, you can tap your fingers, you can play a musical instrument. Whatever you do, the music has to happen directly and immediately. To put it another way, any kind of delay is bad.
Don't Need: Computer Software
There is music software which lets you type music in and then play it back. But you can't compose music this way, because you lose the immediacy. Without immediate feedback, your brain cannot develop intuitions.
(One kind of software which is useful is recording software, which is useful for recording your own compositions and not forgetting them.)
Don't Need: Music Theory
The reason you don't need music theory to compose music is because there is no proper theory of music, at least not in the scientific sense (at least not yet).
There are two kinds of music theory:
- The kind which follows from common sense observation of music
- The kind which goes beyond common sense
Do Need: to Like Music
This might seem obvious, but I will say it anyway. If you don't like music, you won't be able to develop an intuition for music. By the same token, it is difficult, if not impossible, to compose music which other people like but which you don't like.
Do Need: to Improvise and Experiment
You can't develop intuitions about music by playing exactly the same music over and over again. The kinds of intuition that you need are intuitions about how specific variations in musical items affect the musicality of those items.
Don't Need: Discipline
Musical composition should be an essentially hedonistic activity, where you develop intuitions about how to make music which sounds nice. If you have to force yourself to do it, you're doing it wrong.
Don't Need: Ability to Play Music
You will want to play your own compositions. However it is quite possible to compose music which is beyond your current ability to play on an instrument. The compositions will provide the motivation you need to practise playing them.
When you practice playing your own composition, each time you play it better, that is the best performance of that composition that anyone in the world has ever done. This can be more motivating than trying to play someone else's music, where your performance will almost always be worse than the original performance.
(Caveat: this isn't necessarily good advice about how to learn to play a musical instrument, especially if you want to become a professional performer. But the point is that you can start learning how to compose music without having any advance expertise in a musical instrument.)
Do Need: an Instrument Which Sounds Nice
You don't absolutely need an instrument, since you can do melody with your own voice, and you can do rhythm with your hands or fingers (or even beat-box with your tongue). However if you want to do harmony, then you will need an instrument that lets you play three or four notes at a time.
Also, some kinds of music only suggest themselves when you hear the right kind of timbre (i.e. sound quality). Electronic keyboards are a good way to get a large range of timbres, however you might have to spend a bit to get a keyboard which sounds as good as or better than an acoustic instrument such as a guitar. Also make sure it is touch sensitive, and that it has a sustain pedal.
For more detailed ideas about how to compose music, you can read my article How to Compose Music.