Early spring is better because the wounds heal better, you can see if there has been any winter killed branches, and other reasons.
Taking off branches that cross other branches is good - you don't want them rubbing against each other. It is also good to prune the branches that are not growing well (take them completely off or prune them back to where they are growing well) and the branches that are growing well (take them back part way.)
I looked up several sites about how to do it. There are a surprising number that don't explain well but this one does -
https://www.mehrabyannursery.com/growing-guide/pruning/how-to-prune-a-pear-tree/
I might prune an ornamental fruit tree a little differently but most of the steps are for the health of the tree at least as much as for the fruit production.