I'm wondering when my chilli plants start bearing fruit when would be the best time to harvest the fruit when the chillis are still green or when they change colour.
There are some chilis that are generally harvested when green - jalapeño, rocoto sometimes - but in most cases you'll want to wait until they ripen to their final color. The heat is typically present in the unripe green fruit, but the sugars and other flavors that give each variety their specific flavor profiles will not be developed until the color changes. The difference can be quite profound, and I even like to let jalapeños turn red before harvesting because of the flavor improvement.
As to when they are ready to pick, you can cut them off almost any time, but when they are truly ripe they can generally be pulled from the stem with little effort. Wait too long, however, and they'll get mushy.
It depends on the variety. I have jalapeno peppers that I harvest when they are green. If you planted seeds, the packet should have an approximate harvest time in days. I use that as a general guideline as well to figure out when best to harvest and so far it has worked out well for me.