Hi Septimus,
If you go one board down to "Instuments", look down the topics to July15th, you'll see one "Recording Piano". I give some advice there on how to do, but it assumes that you have more equipment than is the case now. I don't record anymore. But before I got into tape decks, mikes, mixing boxes, and tape to CD transfers, (today everything is direct with PC sound card, music files, and CD burners), I used a simple Sony casette tape recorder. It did not have the clarity of my later, more elaborate set-up, but it worked.
Place it about 10-15 feet away from the piano, and experiment for awhile with the volume. Some cassette recorders have a gismo built in that when the volume gets too high at the source, it compensates with a Dolby killer filter that truncates higher frequencies to avoid sound distortion--so the resulting recording seems to lack dynamic range. You have to play with it a bit to ensure it will not get overwhelmed. If you have a grand piano, also experiment with the lid fully open and partly open to ascertain which sounds better.
If you want to get fancier but remain in budget, you could visit a stereo equipment store to explore the more inexpensive options there, or talk to a PC guru on direct digital recording to CD using your home PC.
I applaud your recording your own playing. Every pianist should do that! There is no teacher more demanding than your own critical listening. Often what we believe we're producing at the keyboard is far from the desired effect.