1. If it's art from within the fandom, and you didn't draw it, and it wasn't drawn for you, don't use it to represent yourself or your characters. Period. No exceptions. This includes everything from pulling artwork straight from a Google search, to editing someone else's artwork to look like your character. Don't do it. Ever. Don't use it as an avatar, don't repost it to other websites (including/especially Facebook), just don't use it at all. I promise you won't be the only furry in the fandom without an avatar representing your fursona.
2a. When designing your character(s), never conciously copy any portion of someone else's character. This includes using someone else's character details in your description, but it also includes using someone else's character as a reference image when getting art drawn of your character. If an artist asks you for a reference image or description, and you point to someone else's character and say "he/she looks like that", that is a major faux pas on a number of levels. Similarly, don't say "he/she looks like that, except with these minor changes". No one else's character should ever show up in any part of your character description. The furry fandom is large, but it's small enough that someone who knows the owner of the character you're plagiarizing will eventually find you, call you out on it, and in some cases, get you banned from major furry websites for being an art thief.
2b. Related to the above point, if you find out later that someone else has a furry character with an appearance close enough to yours to cause confusion, the general rule is that the person who's been using the description the longest is the one with the right to continue using it, the other party must change something about their character. Failing that, the person with seniority gets to tell everyone they've ever known and will ever meet to "watch out for so-and-so, they completely ripped off my design and refused to do anything about it". The exception is in the case of highly-generic characters, which is why it's a good idea to make a genuine effort to set your character apart from the rest without relying on something bland like fur color, species, or hair style.
3. Never edit someone else's work for any reason, especially to make it look like your character. I'm not entirely sure why this needs to be said, since it's a pretty blatantly obvious no-no, but it happens with disturbing frequency. When an artist draws furry art, the artist retains all rights to the image unless explicitly stated otherwise. The owner of the character retains a rudimentary, theoretical, unregistered trademark on the character's design, but since that sort of thing has never been legally tested, it's highly uncertain (the usual "characters (c) their owners" line is meaningless BS that holds no weight and defends nothing). That alone makes editing artwork without permission illegal, but in the furry fandom, things go one step further. As I mentioned above, this is a fandom small enough to be somewhat self-policing, if a bit slow at it, so in addition to the legal issues, there's also the fact that you're stealing from fellow furs; you're stealing from the original artist, from the owner of the character you modified, and from the owners of every other character in the picture. Like I said in #1, if it's not yours, don't use it, even if you edited it first. In fact, ESPECIALLY if you edited it first, because it shows that you put concious effort and forethought into your art theft.
4. Speaking of art theft, don't claim that you drew something you didn't draw. Thankfully, this doesn't happen often on FT, but it's a pretty hot-button issue among furries. In a fandom where people can go on TV, make the entire fandom look like a bunch of perverted morons, and be welcomed with hugs and snuggles at the next furry con, there's one thing that can get a person truly shunned from large chunks of the fandom, including banned from furry cons (depending on how many friends in high places the victim has). That one thing is claiming to have drawn something you didn't draw. So please, just don't do it, for any reason.