Oh! Something I'm learning too. Okay, so we just started composition, of course I don't play piano. I actually play flute, so concert pitch and all that. If you're starting from scratch, there are basically 2 main components when composing: theme and variations. So a simple theme would be twinkle twinkle. You can use that theme and do various things to it to make it sound different and musical.
Examples of variations: add notes, remove notes, change from minor to major and vice versa, invert the notes, change articulation, harmonize it, change the tempo etc.
It doesn't need to be fancy but it can still sound great. I recommend writing out a simple theme first and then changing key, time signature etc. This will make it easier for you.
Examples of Themes: twinkle twinkle, are you sleeping, three blind mice, silent night, Mary had a little lamb, Rudolph. Just things like that, old Christmas carols or nursery rhymes.
Website for more info: http://drawmusic.com/HowToWrite/
