His soda was flat, but he drank it anyway.
Tomorrow is my birthday; however, I may not bother celebrating.
I'm sure you've seen examples of "however" punctuated with just a comma, the same way as "but". This is wrong. You're probably asking yourself, why should they be punctuated differently? Don't they mean the same thing? Well, kinda. The big deal is, they're different parts of speech.
BUT is a conjunction. It joins two clauses (or words or phrases). It works the same way as "and", and all you have to do is cap the first clause with a comma. (In fact, that comma's not strictly necessary. You could write "His soda was flat but he drank it anyway.")
HOWEVER is an adverb. It's not a link between the two clauses; it's a modifier that is part of the second clause. Since the two clauses are not joined by a conjunction, they must be separated by a semicolon. (Or a period. You could also write "Tomorrow is my birthday. However, I may not bother celebrating.") In fact, because it's an adverb, its position can shift within the clause: "Tomorrow is my birthday; I may, however, not bother celebrating."
Why is this important? Well, because however has a usage in which it is punctuated the same way as but, but in that case it has a different meaning. Here's an example:
You can't escape, however you try.
In this sentence, "however" no longer means "on the other hand"; now it means "no matter how". That's why punctuation is important; if you punctuate "however" wrong, you change its meaning and mess up the whole sentence!