All 8 Uses of

however
in
The Return of the King

But however that may be, my lord Faramir is abroad, beyond the River on some perilous errand, and he may have sent tidings.†
Chpt 5.1 *

however = in whatever way

Frodo, however, was silent and looked rather sad and thoughtful.†
Chpt 6.8

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.

Frodo and Sam, however, went back to ordinary attire, except that when there was need they both wore long grey cloaks, finely woven and clasped at the throat with beautiful brooches; and Mr. Frodo wore always a white jewel on a chain that he often would finger.†
Chpt 6.9 *

For I have not ridden hither from Isengard, one hundred and fifty leagues, with the speed of wind, only to bring you one small warrior, however courteous.†
Chpt 5.1

Yet the Lord of Gondor is not to be made the tool of other men's purposes, however worthy.†
Chpt 5.1

However that may be, the Captain of Despair does not press forward, yet.†
Chpt 5.4

But however grim they, might be, they seemed to have no leader among them who understood warfare.†
Chpt 6.8

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 contrastand 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)
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?"