As already said, the most important thing is to only apply fitting pressure to the inner or outer race as appropriate depending on whether you are fitting to shaft or housing, you don't want to apply a side force across the bearing race. Dependant upon distance required to push or drive the bearing a suitable socket from a socket set or a box spanner often will do the job. Sometimes with care it's possible to use the old bearing components as a spacer to start the 'push', but be careful not to push to far and jamb the old component on the shaft or in the housing.
To disassemble an old ball bearing race, destroy the race cage, clamp the outer race as hard as possible in a metal working vice with a block of wood below it to stop it swiveling, you are attempting to make the outer race oval, bunch all but one of the balls tight together leaving one in the centre of the jaw gap on it's own, hit this one with a blunt punch to knock it out.
Believe it or not that is the reverse principle of how the balls are put in there in the first place. Some larger races may have a slight scollop in the track rim to aid this.