Maximum Laser Coupling in Optical Fiber

That is a rather broad question really and depends on the type of laser and fiber that you are using.

First you need to make sure that your fiber's end is flat and properly polished (some kits exist to do that). The obvious is use some coupling optics such as a lens or a combination of lenses in order to reduce the size of the beam entering in the fiber (if that is an issue). Now you must make sure that the angular characterisitcs of your focused laser beam matches the numerical aperture (i.e. acceptance angle/cone) of your fiber. You can buy fiber connectors with a lens included in it, or even spherically ended fibers. I would imagine that a tapered fiber is also a good way to couple a large laser beam into a smaller fiber