when i did GCSE music we had to have 2 performances, i'm a pianist but that's all so i had to sing for my other one! i can find the notes but I'm no great singer and it wasn't the end of the world!
our teacher was really helpful with comp advice, starting with basics, like the number of bars being always divisible by 2 (2,4,8,16,32,64 etc...)
then choosing a key and relying on primarily on chord I with your dominant and sub-dominant also used frequently throughout as pianist64 said. but also throw in a few chord IIs and VIs or something!! We used to draw up a basic structure to show bar to bar prgression from I-I-V-I-V-V-IV-I and so on. obviously you can change it but it give u a start to begin filling in a melody and some kind of chord base. then, as was also suggested earlier, make variations on your original theme.
it's actually quite good fun - although the worst bit was writing it all up - it took me HOURS!!!!!