Is possible to fire a Canon 430 EX II (off camera) using a Canon 100D without a separate trigger?
No, it isn't possible just using the camera alone.
You will need to buy additional hardware, or upgrade to a different camera like a 700D, 750D, or 760D which have a built-in master flash mode.
The first resource you should look at for a great introduction to flash photography is strobist.com's Lighting 101. In particular, there's a post there called Synching Your Flash that shows you how to trigger your off-camera flash using just a 1/8" audio patch cord and a pair of adapters. (See also Understanding Your Flash.)