Attribution does not always cover you when you use copyrighted work, however you should attribute or cite sources you use in your writing or creations to avoid plagiarizing. Be sure to be familiar with fair use as you incorporate the work of others into your own.
You should cite sources that you quote, summarize or paraphrase. You should cite any ideas that are not your own. You do not have to cite commonly know facts such as George Washington being the first president. If facts can be found in at least three places, chances are this is common knowledge.
You should give credit to those who inspired you and helped form your ideas. Citing also leaves a breadcrumb trail for those who read your work to see whose work you used. Others may want to refer to those works for their own research.
There are several style manuals. Students should check with their teachers to see which manual they prefer. Authors are normally told by publishers which manual to use.
A few common style manuals that you will find in most any library are:
Here is an excellent tutorial on the principles of paraphrasing from the Harvard Graduate School of Education: