Hi novice, welcome to the forums!
When: Anytime. Winter is ideal but summer is ok too.
Where: It depends what you want to do! Are you removing branches, shortening them, trying to make them grow another direction, taking cuttings?
As for the bud thing, this is relevant to ornamental shrubs like roses, climbers and fruit trees, where fine shaping is desireable, not to pruning a large tree's branch off.
I can't think of any occasions where the advice is to cut just before a bud (I'm sure someone here will!), it's usually after a bud.
The key point about the cut in relation to the buds is that when the branch is shortened, it should regrow from the last bud or buds (I'm generalising here: most trees behave this way if you cut growing tip of the branch, willows included).
If the last bud you leave on the branch is facing downwards and towards the trunk, that could encourage an ingrowing or otherwise less than ideal branch.
If the last bud is facing up and away from the trunk, the new branch should grow straight out.
But if you are cutting most or all of the branch off, this is not an issue.
Just read up on how to cutt off a tree branch and go for it: willow can take anything you throw at it.