What sort of project are you looking to do?
Fibre optics is just a way of carrying information, so the possibilities are endless really. You could try and build something that transmits music from your stereo to another room in your house, for example. Or you could try and send information down a fibreoptic cable from your computer.
Telephone signals are carried by fibreoptics over long distances, so a telephone that used a fibreoptic cable instead of a normal copper wire lead would be pretty cool. A bit pointless, but cool.
Is the project for any particular purpose (school, college?) or are you just looking to have fun?