First of all if you are going to copy someone else's material you must ask permission first. This means contacting the author or the publisher and asking them for reprint rights. However sometimes the availability rights are printed right on the article along with information that you must credit to the author. This could include the date of original publication, where it was first published or the name of the publisher if it is from a book. Some articles may not be quoted or reprinted from unless you also provide a link to the URL of the author's choice.
Crediting an article to its rightful source is called attribution. You must always attribute the work of others and you must do it every time you quote from the article. This is true of direct quotes and paraphrasing. You can't condense someone else's writing and then assume that the readers will know that it belongs to ideas that are quoted earlier on in the article. That is called plagiarism.
Another important copyright issue is “fair use.” This is a legally defined terms that allows U.S. citizens to copy and distribute the work of others as long as they adhere to certain legal terms. For instance, in the United States bloggers are allowed to quote sentences and short passages as long as the quote is credited to the author.
However giving credit is sometimes not enough and length may have a great deal to do with what you can replicate on the web. For instance you cannot copy and distribute your favorite piece of music through a web blog. Also laws vary from country to country. Don't fall for the common myth that it is somehow all right to copy material by writers from other countries just because it is the Internet.
