I am a newbie comic reader who needs some help!
My wife got me "Final Crisis: Legion of Three Worlds" as part of a set of books for my birthday!
Hello! Welcome to the hobby. As you might expect, falling into comics, especially those with decades of continuity such as the Big 2 of DC and Marvel, is never going to be easy. You just sort of have to muddle your way through in the beginning.
The Legion of Super Heroes is one of those properties that has some of the most convoluted backstory, due in part to how long they've been around (since 1958) and an because they've gone through several revisions and reboots over the years; Part of this is a side effect of being set in the future and having to readjust for changes in the present (example: can't be inspired by Superboy if he never existed!)
The basic gist of the Legion is; They are a group of young super heroes a thousand years in the future who have banded together to protect Earth and the United Planets. Generally, they've gotten their inspiration from Superman or Superboy, so they tend to adopt his principals; i.e. no killing. Each member tends to have a single power, one that is usually the result of an accident or their place of birth.
Legion of 3 Worlds, as some of our fellow thread members have described, is a tie-in to Final Crisis in the loosest sense. All you really need to know is that Superboy Prime is a version of Superboy who went down an evil path; He tends to be immensely powerful and usually an existential threat when he pops up. In Legion of 3 Worlds, it becomes apparent that he is too much for them to handle alone, so they call upon other Legions, from other realities, to help them. This is a nod towards and an attempt to reconcile the different versions and acknowledge they all existed.
tldr: Superboy Prime is an asshole and the Legion calls in other versions of themselves to help fight him. You won't know most of the heroes and villains involved, but it's still a very entertaining story! Hope you enjoy!
Is there anything else I should read before I read this, and does this story continue anywhere after this book ends? I guess I want to know if this can be read as a standalone book or should I buy some previous volumes to get a better idea?
There is no real direct continuation to Legion of 3 Worlds; However, if you end up liking it, I'd recommend "Superman and the Legion of Super Heroes" as it was also written by Geoff Johns. Legion is difficult to get into. I'm an enthusiast so I'd love it if more people read them, but going back is extremely difficult. There are "Essentials" or "Archives" that collect older versions of the Legion stories for cheap, but you're talking 1960s/1970s Legion.