WELL,
there are a few places to start:
-Practice Being Creative
-Learn Music Composition Theory
-Learn Music Production Theory
-Get a sequencer/DAW
The first one you can do by grabbing an instrument. (If you don't have at least a keyboard, skip this step). Even if you can't play the instrument well, keyboards especially you can use to just figure out the notes of the music that's in your head.
The second one is what I think is the most important. Whether it's formal or informal, knowing WHAT THE HELL you're writing down helps A LOT. Learn how chords, scales, notes, melodies, rhythms, and arrangements work. You can do this by taking classes, or if you have a sequencer with MIDI import capabilities you can look at MIDI's of video game music to see what it's made of. (Or if you can, read lots of sheet music of giant expansive orchestral symphonies. )
The third one is very tricky. This is more technical where you start learning about compression, EQ, mastering, balancing, and general soundscape. This definitely isn't something easy to learn on your own, because it's very difficult to pick out your own mistakes when you start out. I suggest reading this guy's guide. It's a great place to start to learn how to make good drum lines, work with acoustic instruments on software, and general production values.
The fourth is the absolute most important if you wanna get anywhere in the world of computer music. You need a good software. Here's a list of software I know of that people like:
-FL Studio (i personally recommend it)
-Reason
-Logic Studio (for Mac)
-Cubase
-Sonar
-Ableton Live
-Finale (standard sheet music notation)
-Reaper
-Audiotool (Audiotool is a very limited online sequencer that runs on flash. www.audiotool.com runs right in your browser)
There are lots more out there, but these are the most frequently used (by OCRemixers and by professionals catalogs.) Try the demo's for each one and use the one you like most. (Having a DAW you're comfortable with is important.)
What the software is for is to write down stuff and hear it at the same time on instruments/synths of your choice. No one has hi quality stuff at the start, but if you have money, I recommend buying stuff like:
-Komplete 6
-KORE 2
-(if FL studio) Sytrus (in my opiniong the best synth in the world)
-East West Composer's Collection
If this stuff puts a dent in your budget, don't bother with it. Stick with the free/cheap stuff. It won't be good quality, but practicing for yourself is more important. Save up for this stuff and it'll be worth the effort.
After you find your software, it's good to have some good hardware. I don't know much about good hardware, but if you check the "Guides and Tutorials" forum in the Workshop section, it's overloaded with helpful info.
As for REMIXING music, what's done here at OCR is taking a VGM source tune and expanding on it, just putting it in different instruments doesn't really cut it. It has to be something that shows a lot of effort was put into it to make it stand on its own as a good arrangement. What you can do is compare OCRemixes to their source tunes, and then try to make your own interpretations. Good ways to do this are imagining source tunes in totally different styles/genre's. Sometimes for me, adding a simple swing rhythm to an otherwise upbeat techno VGM tune gives birth to some great latin jazz rendition in my head.
Also, KEEP PRACTICING!!! Nothing will ever sound awesome when you start out (For two years, I couldn't make anything decent.)
Hope that helps.
EDIT: This might sound super intimidating, but you should realize music isn't something to be taken lightly or learned quickly. Some people still can't get it after years of practice. It takes talent, but that's not to say a lot of people don't have talent. If you like OCRemixes and want to do them, work for it and the practice/experience helps you show your talent.