I think that the biggest barrier that keeps most people from composing is a lack of confidence. I've even met very talented musicians with confidence issues. Mostly though, I've heard people say they can't write their own music because they don't know enough about music theory. That is a big, fat load of bull. I'm here to tell you that you can make music to call your own. Don't listen to what other people say. If you can hit some notes on a keyboard, or you know some chords on your guitar, then you can write music. I started composing music before I knew anything about theory or recording, but through making music I learned just about everything I know today.
By the way, when I say 'composing' or 'making music' I'm not necessarily talking about busting out sheets of blank musical staffs and diligently writing down all the notes of your masterpiece. I might as well tell you to get one of those ruffled shirts and a jacket with long tails before you sit down to compose. There is nothing wrong with writing music using that method, but don't let anyone tell you that that is the only way to compose. If someone did tell you that, they're lying, and it is your civic duty to light their pants on fire the next time you see them. If you somehow make a sound that is uniquely yours, you just composed something. See? Easy!
So lets just assume that you've agreed to go ahead and start composing music. Depending on how you want to do this, you could read my articles Picking out an Instrument and/or Make Your Own Recording Studio. Once you either learn to play an instrument at least a little or have an awesome small home studio ready for input, or both, you can come back and REALLY soak in this article.
I know I was encouraging you a few paragraphs ago, but lets just get this out of the way: the first songs you compose probably won't sound so great. Learning to make your own music is just like learning to play an instrument; it doesn't sound all that great in the beginning, but that's because you're new and practicing. When I started making music on my computer, my rhythm was terrible, sound quality was bad, and everything was in C Major only because I couldn't figure out how to use those little black keys. I even still have some of these old pieces on my website, which you can listen to when your starting out, so that your own music can at least be better than something.
The important thing to remember about composing is that you need to compose! Compose and produce and perform your music all the time. No one needs to hear your first recordings besides you. I guarantee you'll be surprised with the results of at least one of your first few efforts. It'll sound way better than it should, and you'll look back when its done and think "Wow, that's actually not completely terrible!" One of my first songs ever was this. When I wrote it I still knew nothing about music theory and had only written a couple of songs before it, it's a very simple and repetitive song, but it does convey a feeling and is relatively polished. I was as surprised as anyone when it was done. Once you've made your new song as good as is reasonable, record it if you can, then leave it and start a new one. The more you compose, the better you will get at your technical skills and your technique.
There's a voice in your head, we all have it, that says to you "You shouldn't even bother, whatever you make will sound really bad. And what if someone else hears it? That would be a nightmare! Just give up now and watch reality shows instead. I love that one with the clown and the cheerleaders." The most important thing you can do for your composing and maybe for your whole life is learn to ignore that nagging, doubting voice in your head. When is the last time you ever thought, "Wow, thanks self-doubt! I almost did something new! That was close!"
Once you've started composing and have successfully tuned out ugly self-doubt, then there is absolutely nothing in the way of making some fine music that others will actually enjoy. If someone like me, with so little real training and even less natural talent, can do it, then so can you. Send some of it my way when its done.