Doping is adding atoms to a material to modify the conduction properties, for example to make an N type conductor or a P type conductor.
Diffusion is allowing atoms of one material to move by heating it enough that the atoms can move to other positions. One can dope silicon by putting arsenic (or other dopants) on the silicon surface, and putting the silicon wafer in an oven at a temperature that allows the arsenic atoms to diffuse (or move) into the silicon and modify the conduction properties. By choosing the proper temperature and diffusion time it can be possible to control the depth and concentration of the arsenic in a way that is useful for making a desired semiconductor device.
Ion implantation is making a beam of energetic ions and allowing them to hit a surface made of some material -- a material different from the ions. It is used to modify the properties of the material being bombarded. It can also be used to dope semiconductors. The high energy of the ions can damage the lattice structure that is being doped, so it is usually necessary to anneal the semiconductor by heating to allow it to "heal itself". Ion implantation can also be used to harden metal surfaces or change their friction properties by choosing the right type of ions to implant.