The first rule of pruning is to remove the four Ds. Dead, Dying, Diseased and Damaged. This is best done in winter when you can see the problem. Aftr that prune for reversion and tidying.
Secateurs, Pruning Saw, Gloves
For larger branches, remove any obvious dead, diseased or damaged wood, cutting back to live wood using a clean saw.
Smaller shoots can be cut using clean secatuers cutting back just above an outward facing bud.
A green shoot on a varigated shrub needs removing at its base. This is known as reversion and any all green shoots are stonger and eventually take over, changing the look of the plant.
Remove old flower heads from plants like lavendar in spring to allow room for new growth.
Growing a Lily in a Container