Saving chilli seed (and their sweet pepper/bell pepper cousins) is relatively straight forward. As the chilli was already at its final colour and of the right kind of shape for this variety, all I had to do was to carefully separate each seed from the rest of the fruit and leave them on a small saucer on the windowsill to dry.
I ended up with 24 viable looking seeds, plus a couple of misshapen ones which I discarded. I don't think these latter 2 would do anything - one had a hole in the middle and the other was brown and shrivelled. I left the rest to thoroughly dry for 10 days and I've just tipped them into a small paper packet (or you can make your own), sealed it, added a label and put it in my trusty seed tin for its winter hibernation. Time will tell what kind of germination rate I'll get.
I'm relatively new to vegetable seed saving (having only saved borlotti beans previously), so I've found this book by Sue Stickland to be a good value introductory guide to chilli seed saving and a whole host of other possibilities.
NB Before you start any seed saving activities, check that your variety is an open pollinated one (so the plants from your saved seed will be like their parent chilli plant) and not from an F1 variety (the offspring will be variable and most, if not all of them will be nothing like their parent plant and the seed may not be viable anyway). Most seed from commercial suppliers should have F1 clearly marked on the packet where applicable. Avoid anything with Plant Breeders Rights (PBR) too as you're not allowed to propagate any of this type of plant material whilst PBR operates.
If the chilli you're saving seed from is a hot one then you'll also need to think about wearing gloves and/or goggles to prevent any potent juices getting onto your hands or into your eyes.