All 5 Uses

however
in
Saving the World and Other Extreme Sports
(Auto-generated)

However many you can eat without barfing.
Part 3 *

however = whatever number of
Some of the mutants, however, didn't seem to have gotten Angel's latest memo and were still fighting one another, and us too.†
Part 4 *

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
However, in an interesting, nonflying change of pace, we were driving.†
Part 1
However, they were broadcasting the earnest face of a fair-haired woman who was speaking in consecutive languages.†
Part 3
However, since they were evil, basically we saw stuff that would fuel the world's nightmares for the next five hundred years.†
Part 4

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?"