Understand the scope of copyright law. It does protect literary works, paintings, photographs, drawings, films, music (and its lyrics), sculptures and many other things. Except in literary fiction, it does not protect the underlying ideas, and it does not protect facts. For example, copyright doesn't prevent you using ideas and facts found in a book or journal you read, though common courtesy requires that you attribute the original authors.
It doesn't need the symbol © to be copyrighted. Understand that nearly everything on the Internet, and everywhere else, is copyrighted, by default. "I found it on the Internet" is not a defense against copyright infringement; works on the Internet are as copyrightable as any other kind of work. Nor is "it didn't say it was copyrighted." In nearly all jurisdictions, it is not necessary for a work to have an explicit copyright notice for it to be copyrighted. It is also not necessary for copyright in a work to be registered; this simply makes it easier to be compensated in court. Without an explicit dedication to the public domain, assume that it is still under copyright.
Understand the difference between copyrights, trademarks, and other forms of "intellectual property." The term "intellectual property" itself, and the kind of thinking it encourages, has led to these very different things being confused with each other. Trademarks forbid using certain words, marks, symbols, and so on within certain contexts, to protect consumers from misrepresentation. Copyright would not prevent you from, for example, writing some new text editor software and calling it "Microsoft Text Editor", but trademark law would.
Understand that one does not get a copyright without some creativity. If you ever wonder whether a certain action would infringe on the copyright of someone else, the question to ask is: is this a creative work on my count, or am I simply drawing from the creativity of someone else? Lunches, as any economist would tell you, are not free. Some examples: a new copyright over anything. You cannot scan a photograph from, say, a magazine and then put it on the Internet; the copyright would still reside with the author of the work. The flip-side of this is that scanning a work which is in the public domain would not, in many jurisdictions, give you the copyright over the resulting scan. This does not generate a new copyright. This would be a derivative work of the video or computer program. For example, a plain text logo in a generic font. Neither are simple geometric shapes. But don't rely on this unless you are certain.
Learn about the Public Domain laws for your jurisdiction. "Public domain" is short-hand for "uncopyrighted", not "publicly distributed". A work can be out of copyright due to age, by the nature of authorship, or other reasons.
Understand what "fair use" is, and what it isn't. Called "fair dealing" in many jurisdictions, fair use is simply a guarantee that copyright laws do not infringe freedom of speech and make critical commentary impossible. It permits, for example, limited quoting of copyrighted material. In some jurisdictions, it would allow creating a copy for personal use (such as a backup). It is not a blank check granting you a right to do anything at all and call it "fair use." Fair use is an extremely complex body of case law; it is often very difficult for non-lawyers to tell in advance whether or not a certain use will be considered fair use in court. If in doubt, seek permission first.
Understand the law about derivative works as pertains to fiction. It was said above that "ideas cannot be copyrighted." This is not entirely true; fictional characters, story-lines, and settings can be copyrighted. This means that fan-fiction, drawings of characters from copyrighted works, and so on are all technically copyright infringements. Sometimes copyright holders turn a blind eye to this sort of thing, but unless it has been explicitly authorized, don't count on this being the case.