Use your own voice when you write. Paraphrasing another person's work by simply switching the words is a form of plagiarism. For example, if the document you were working from said "Dogs, a species descended from the wolf, are carnivores," it would be plagiarism to write "A canine, an animal derived from a wolf, is a carnivore," because you have simply changed a few words. However, taking ideas from the document and putting them into your own voice is not, as long as you appropriately cite the ideas you have drawn from. For example, you could rewrite the above sentence "According to "Name of Source," wolves are carnivores, and since dogs are in the wolf family, they too are carnivorous animals." In this case, you have taken an idea and given it a new spin, without just regurgitating what someone else wrote, and given credit to the original author.
Attribute ideas. If you borrow from another work and give credit to the author, it usually will not be considered plagiarism (unless you regurgitate an entire paper). For example, if you take the idea that dogs are carnivores from National Geographic, you could write "According to National Geographic..." You'll still want to use your own words and voice, but by attributing the ideas you derive from someone else's work, you'll be doing an even better job of avoiding plagiarism.
Use more than once source of material, properly attributing any ideas you get from each. If you copy from only one document, the chances are higher that you will be accused of plagiarism since you only have one source to draw from and you may accidentally take more ideas than you should. However, if you have two or more sources, you can derive information from both to help you create a new perspective on the issue, while giving proper credit to the sources that inspired you.
Add your own ideas. While it is OK to draw research and material from a document, you can avoid plagiarism by taking the ideas presented in your source material one step further. Put your own spin on the topic, make a statement about the opinion the work is drawn from, and add something new to the subject.