It kinda looks like you got all you needed about pruning but I saw that no one warned ya if you cut your holly back a lot it can take up to two years for it to come back and you shouldn't cut lower branches either.
That depends on the type of holly you have. For most holly shrubs you just have to prune the tips of new growth in autumn or winter. You can use either loppers or pruning shears. Stay away from hedge trimmers because it tears leaves and the bush looks ugly later.
I always go in and cut out dead and spindly branches first. Then I cut behind the new buds so that any holes will fill in during the next growing season. Pruning holly shrubs is relatively easy though I agree with the other poster that you should know the genus.