Hey man, I was the exact same way (although I had a good ground with band music for several years before I started and plenty of classical appreciation as long as I have lived).
My biggest tips are-
1. Check out existing works... an AWESOME place to do this is IMSLP, a library of free classical music all the way back to Medieval and even Ancient tunes. You can download the scores and follow along as you listen once you master the basics of theory (AMAZINGLY helpful).
2. Get some resources together. I see Music Theory.net is already up there (awesome resource for beginners to intermediates), but also check out the Garritan Rimsky-Korsakov course on Orchestration and Composing once you have done a bit on mt.net (I also recommend doing a few of their exercises/quizzes).
3. Start with Emulation- find a composer you like, OR someone on Newgrounds (if you do the latter, you can ask them to send MIDI files of their work even) and really study their music- find a style they seem to have- dissect their music and find what things they like to do (e.g. rips on horn; pizzicato sections; timpani parts in transitions). Then, try to write a piece similar to that. Emulation is great because you are working towards a goal that is very clear and ready to visualize.
4. Find people knowledgeable in theory in your community or area or take some courses in school if possible- even getting some quick lessons and discussions with friends into composing is a great help!
May I ask if you can "think up a melody" on the spot? If you can, definitely keep up with working towards composing.
Consider starting with a free program- I started with LMMS, which is a good electronic program, although I used it for orchestral using Soundfonts (a form of virtual instrument you can find online for free in places). If you want to get extra practice, try writing pieces by hand for a while until you feel comfortable doing that before moving to a notation program.
It also helps to know the keys of the piano if you don't already.
If you ever need help or some crash-courses and can't find any or get enough info from mt.net, you are welcome to PM me or add me on skype (lord-samulis) and I'd be glad to help you as best I can.