This article is from the RSC/UKSC Cricket FAQ, by Ganesh with numerous contributions by others.
PROPER sports shops to put them on for a small charge
using a sort of cone. You may be lucky similarly.
Other-wise roll the rubber up into a doughnut and then
FORCE the rubber over the end. Once you've actually got
the rubber over the end of the handle you just unroll
the rubber along the length of the handle and smooth
it down. It works well, especially with a twisting
motion with both hands using downward pressure towards
the bottom of the handle.
As it turned out, I actually got them on quite easily.
A (girl) friend of my wife got a disposable plastic
shopping bag, poked it through the grip, then used
the handles on the bag to pull the grip on the bat.
It went on reasonably easily. Then I rolled the grip
from each end and cut out the shopping bag.