Select an LED or LEDs based upon the light output and light distribution needed for the application. The LED specifications will outline the light output, electrical requirements and thermal and mechanical interface for the LED. Some applications requiring high levels of illumination may need more than one LED.
Select or design drive electronics that will convert the AC line power to the current-controlled DC power needed for the LED. Most electronic drivers will not be compatible with conventional dimmers, so take care to investigate dimming schemes if that's desired.
Attach the LED package to a heatsink. Good thermal contact is important. If the temperature gets too high, all bets are off --- light output will decrease and lifetime will be short.
Integrate the package into secondary optics --- whatever reflectors, lenses, or diffusers are needed to shape the light to meet the need. This can be a complex process. LED fixture manufacturers use nonlinear raytrace programs to maximize efficiency and be certain they don't throw away too much light.
Put the whole package in a mechanical assembly that is attractive and functional. Industry players put a lot of effort into this step and it will be difficult to duplicate their process at home, but home-made designs can have their own charm.