Pruning a tree is not like trimming a hedge, although a seriously overgrown hedge is basically a row of scrubby trees that could need pruning to restore it to a proper hedge again.
Young ornamental trees may be shaped using secateurs to prune side shoots, but removing branches on an adult tree will need a special pruning saw or saw blade for your bow saw.
Winter is usually the right time to prune a tree.
Why is winter the best time to prune most trees?
Some trees will bleed sap if they are pruned in spring. This is not likely to kill a healthy tree, but it's best to avoid it.
Birch, Laburnum, Hornbeam, Lime (as in Tilia, the common roadside tree, not the citrus, nor the Roman infrastructure, and certainly not the scooters) and Poplar trees are all potentially heavy bleeders, so they are always pruned in late autumn to early winter for this reason.
Magnolia and Walnut trees are pruned in late summer. The Walnut may lose some sap at this time, but within a year it will have healed more than it would a year on from an early winter pruning.
That said summer is often a fine time to prune as well.
Flowering cherry trees and many stone fruit trees (i.e. cherries, plums, peaches - these are all in the group Prunus) should be pruned in summer only.
This avoids the risk of Silver leaf disease, which spreads in winter.
As for pretty much all other trees, pruning them in summer or winter makes little difference.
If a tree needs pruning to remove Dead, Diseased or Damaged wood, it is usually best to do it right away.