All 4 Uses

however
in
The Pregnancy Project
(Edited)

Meeting with Network 3, however, is when things got interesting.
p. 171.3

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
As I tried to pull myself together, Mr. Greene told me that he would help me however he could, and that I didn't need to worry about everything at once.
p. 174.7 *

however = in whatever way
The comments, however, got heated at times and cruel at others.
p. 182.7

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
However, the day after the school's superintendent declared her valedictorian, the principal announced that she was going to have to share the honors—he was appointing a covaledictorian who had a slightly lower GPA.
p. 213.9 *

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?"