A lot depends on context, tone of voice, etc, but if you say "I finished that book last night" (or "I finished reading..."), most AmE listeners, in a normal context, would assume that you read it through to the end. (Note, this is assuming that the conversation is not somehow of an ironic nature, and the book is some sort of narrative. If the book is something like a physics book you may just mean you finished the chapters relevant to the current discussion topic.)
Saying something like "I'm done reading the book", however, is a hair more ambiguous, and if the person uses "air quotes" around "finished", or says the word with a sarcastic tone, one can assume that the book was not read through to the end. (For this reason, knowing the context and tone of speech is important.)
Also, if we are talking about some time in the past, the person might say "I read that book", implying that they had read the book all the way through, or at least felt that they had read the important parts and "skimmed" through the rest. (Be truthful now: Have you ever read any book longer than about 100 pages and not just "skimmed" some parts of it?) An honest speaker would say "I read parts of that book" if, indeed, they had not (to their recollection) read (or reasonably skimmed) the entire thing.