Actually, you learned to speak before you learned to write English, right? You can, and should do music the same way. Sing an idea to yourself, just dum de dum la la la. Then, sing it on tape, or get a recording program like audacity, so your computer can record it. Now, here's the tricky part, write it down. Make up a language to write it in, just for yourself. Now, put it away for a week, then bring out the written copy. Try to sing it again from the written copy. Listen to the tape and see if you got it right. That will teach you to read music right there. It will tell you what you need to learn and then you will know what to look for when you follow Hattiebod's advice.
You can write complex instrumental pieces this way with a "midi editor". Basically, these are programs that let you select the notes with various interfaces other than sheet music with the clefs and the "every good boy deserve fudge" system. But you still will be learning A system of SOME kind to notate things. After all, if people are ever going to hear your piece, someone or something has to play it, so you have to communicate with them somehow. Actually, any good scorewriter program imports midi, and writes it out in noation for you. Try the different free ones; there's some really neat "assitants" out there, where you can start with partial notes, etc., and it guesses at what you want for you.
Eventually, you will want to study music theory and musical form, so you have an idea how to turn your basic melody into a symphony, but this method is more intuitive, and actually is preferred for composers, so as not to bias them to the traditional music which is what notation is designed to notate easiest.