Hi!
There's different approaches to this: You can, of course, just use the tools you have now, grab a piece of (musical sheet)paper and a pen and write down chords, notes and harmonies you like and bring them together to a full musical piece. There's some software where you can do that digitally as well, the pro of those is that you can hear what you enter, which is especially useful if you have more than one instrument, for example, so you don't have to ask someone to play it with you. Those are softwares like Notion 6, MuseScore 2 etc. I'm sure you can find one that's free, even.
For recording you might not need anything fancy, in that case I'd quickly download Audacity, it's simple software and it's free, so trying it doesn't hurt.
The more high end recording software I usually use is Pro Tools, but that gets really expensive really fast, however most professional recording studios have that software at hand and their equipment resonates best with it. But that might be something you want to consider further down the line.
Normally every DAW (Digital Audio Workstation) also has a recording function. And that gets me to my next point: DAW's those are fully equipped digital studios. Personally I use Propellerheads Reason, but other big names are Logic Pro (Mac only), Ableton, Cubase and FL Studio. A DAW usually costs quite a lot (200-1'000 range) and it costs even more once you need more plug-ins (VSTs/Rack-Extensions). Some DAWs are usable without any plug-ins, Reason being one example, other DAWs are basically an empty shell without them and you'll end up spending another 1'000 bucks or so, just to get it to a good, usable state.
What are DAWs good for? Well, they let you achieve believable and good sound without (m)any real instruments. You have a wide range of synthesizers you can program and big sample banks of professionally recorded instruments and sounds that you can use to create your musical piece.
DAWs are always compatible with Midi keyboards, so you should be able to use your DGX-205 with any of them and directly play on the instrument you have selected in your DAW (given you have the PC Driver for it).
My personal recommendation is: Use free software like Audacity and a sheet music software first, and if you reach your limit, then consider buying a DAW.
It all really depends on what kind of music you want to make aswell. If you want to compose a complete orchestral score you'll need a DAW eventually, unless you have the money to mobilize an entire ensemble. If you want to produce electronic dance music or modern pop music you definitely need a DAW.
However, if you just want piano music with a bit of singing on top you don't need any fancy tools, then it just comes down to your own idea and execution. There's a number of musicians who became successful by recording something in their bedroom with just their guitar and voice.
I hope this helps at least a little. Good luck on your musical journeys!