All 5 Uses

however
in
Charlie And The Chocolate Factory
(Auto-generated)

But a toothpaste cap-screwer is never paid very much money, and poor Mr Bucket, however hard he worked, and however fast he screwed on the caps, was never able to make enough to buy one half of the things that so large a family needed.
Chpt 1

however = regardless of how
But a toothpaste cap-screwer is never paid very much money, and poor Mr Bucket, however hard he worked, and however fast he screwed on the caps, was never able to make enough to buy one half of the things that so large a family needed.
Chpt 1
Then Mr Prodnose's factory came out with a chewing-gum that never lost its flavour however much you chewed it.
Chpt 4 *
But there was one other thing that the grown-ups also knew, and it was this: that however small the chance might be of striking lucky, the chance was there.
Chpt 7
However long this pig might live, We're positive he'd never give Even the smallest bit of fun Or happiness to anyone.†
Chpt 17

Definitions:

(1) (however as in: However, complications may...)
though (or another expression that connects contrasting ideas)

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 exists, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (however as in: However much she tried...)
to whatever degree (regardless of how much; or whatever unspecified amount)
(3) (however as in: However you do it, get it done!)
in whatever way
(4) (meaning too rare to warrant focus)
Much more rarely (and arguably incorrectly), however can be used to intensify the word how, as when one says "However did you find her?" Grammarians would suggest using two words for that usage: "How ever did you find her?"