When should you prune a Cleveland Pear tree that was just planted last year? And how much trimming should be done?

You should be able to trim the tree during its rest period (typically after foliage has dropped or early spring before new buds form). The art of trimming is generally left to the eyes of the beholder. Trim to help develop the shape you want. It's a good practice to trim lower branches to allow for access under the trees during mowing or mulching chores

Unless the tree is really out of shape, I have never pruned these trees, untangle the branches after a storm, or windy day, that is about it. Of course you must get rid of dead branches, broken ones, etc. If deer are in your area, feel free to spray them with a repellant. Other than some tree food everynow and then, they are quite content trees.