1. The RGB approach
The output from several different LEDs, typically red, green and blue, is mixed. This can be done by combining packaged emitters with suitable optics, or by placing 3 individual chips inside the same package.
2. Phosphor downconversion
The light emitted from an LED chip passes through a phosphor material which "downconverts" a portion of the light. The phosphor absorbs the light and re-emits it with a lower energy, which means the light has a longer wavelength.
Light from the phosphor mixes with unconverted light from the LED chip to form white (if the phosphor has been correctly chosen).
The most common example combines a blue LED chip and a phosphor emitting in the yellow region of the spectrum. Other phosphor mixtures have been developed, such as those that emit light in the red, green and blue portions of the spectrum when stimulated by an ultraviolet (short wavelength) LED chip.
The "blue chip + yellow phosphor" combination is deficient in the red part of the spectrum, so new phosphor mixtures employ other components to providea full spectrum appearance and the possibility of "warm white" light.