All 4 Uses

however
in
The Watsons Go to Birmingham--1963
(Edited)

If you were happy with your son the way he was, this might be pretty bad. However, if you've always wanted a child from south of the border, you might be happy with the new young Mr. Watson.
p. 93.8

however = but (a word used to connect contrasting ideas)
Dad's hand touched a knob that had "Start" written on it, but before he turned it he pulled his hand back and said, "First, however …."
p. 115.9

however = on the other hand (used to connect contrasting ideas)
Grandma Sands called a couple of times and told them that the police thought two white men drove by in a car and threw it in during services, or that they'd already hidden it in the church with a clock set to go off during Sunday school. However it got in the church it had killed four little girls, blinded a couple more and sent a bunch of other people to the hospital.
p. 191.6 *

however = in whatever way
The characters and events in this novel are fictional. However, there were many unsolved bombings in Birmingham at the time of the story, including the one that took place at the Sixteenth Street Baptist Church on September 15, 1963.
p. 209.1 *

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

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?"