On the face of it, the best way to learn to compose is to start composing! Get a free/cheap music notation program like MuseScore or MusicMasterworks, and start experimenting. See what you can come up with. I guarantee that you'll learn a lot about tonal relationships, phrasing, melody, and rhythm just messing around -- and you might come up with some cool tunes, too!
But if/when you decide to get serious, consider the following:
Composers aren't necessarily musicians, nor are musicians necessarily composers. The difference between a composer and a musician is the same as the difference between a writer and an orator. One is tied to the other, indeed relies on the other for their art to come to fruition; but the skills they employ and talents they must have are actually quite different. Seems pretty obvious but it's good to remember because the line between the two sometimes becomes blurred when thinking about music.
You need to know music theory to compose music for the same reasons that you need to know rules of grammar to write. You don't need to learn music theory to play music, but composition is not the same as performance.
What is a musical composition? At the most basic level, it's a set of instructions to musicians. What is music theory? In large part it's a definition of terms, so that musicians can communicate musical ideas using spoken or written language. As you can see, they aren't the same thing; but they are related.
When you play music, you are communicating your musical ideas directly, with sound. But when it comes to composition, you're communicating your musical ideas in writing. A musical score, after all, is nothing more than musical ideas written down. That's why it is preferable to know music theory if you wish to communicate your musical ideas to other musicians.
It is not actually mandatory to learn an instrument if you wish to compose music, but it's pretty hard to imagine composing without it. When you're composing, a musical instrument becomes a tool of calculation aside from anything else. ('Does this interval work? Assuming I come from this harmonic relation, can I go to this harmony?) Theoretically you could just use your voice, but this begs the question of how you'd test multiple tones, harmonic relations, etc.
Time signatures are used in almost all western music, whether in common time signatures like 2/4, 3/4, or 4/4, or more complicated time signatures like 7/8, 11/8, 13/8 15/8 17/8 etc. The good news is that most western music is in 2, 3, or 4. The even better news is that virtually all time signatures are broken down into subgroups of 2 and 3, so even if it sounds complicated, it's pretty easy (conceptually, at least.) To be a good musician you need a solid understanding of rhythm and tempo. As a composer a good sense of rhythm isn't necessary, but understanding tempo (particularly tempo restraints on various instruments) is crucial.
As a musician, it is imperative to study rudiments of percussion. Being able to play on time and in tempo is as important as being able to play in tune. Composition wise, it is imperative to learn what is possible percussively, as well as melodically. You'll also want to learn harmony, including chord structure. While you're at it, learn the 'Church' scales (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian) and the Pentatonic scale.
Learning all this will allow you to communicate your musical imaginings more succinctly and clearly, and also enable you to compose music much more swiftly. One last point about musicianship and composing: you don't have to be a good musician to be a good composer. You need to understand how instruments work, how tempo and rhythm and all the rest works, but you don't have to be good at playing. You just need to know how it works.
If you wish to learn orchestral composition, there's really quite a lot to it. You must think of the level of musicianship your piece requires. If you write a piece that requires a lot of virtuosity, it (at best) will be a shining goal for the musically inclined, and (at worst) almost never played because there's not a lot of people who can play it. At a more granular level, you must be aware of the range of each instrument you're writing for, bearing in mind that range varies both by musician competence and band or orchestra competence. (The expected range of junior orchestra is much different than that of the London Symphony Orchestra, for example.) Possible instrument voicing will vary considerably according to venue, and nuanced volume/instrument changes within the composition might be lost if the piece is to be performed outdoors or in an acoustically disadvantageous environment such as an indoor arena. It is not unusual to receive requests to score specific voices for different instruments, re-score the entire piece for a different type of musical group (i.e. band/orchestra/octet/quintet/trio/choir), or to rearrange the piece in a different key.
tl;dr: Get a free music program, mess around and see what you can do. Consider it the first step in the journey of a thousand miles.