Hi Sam. Bit of advice from my own experience, don't just go willy nilly designing off the top of your head. The best thing to do is use the competition sites like Becky suggested for the briefs or get someone you know, ideally with a bit of creative thinking, to give you a brief.
Designing from a brief is far better than designing a random fictional logo that you've thought of, as when you design something on your own you might like it and feel it's finished but in most cases it's not. Getting the feedback from the person who gave you the brief will give your design a better sense of direction and in the end a better result.
Michael's suggestions is also a favored method by many, and you could also try sending you redesigns to the company to get their feedback, you never know it might lead to some work!