How is it possible to use images without the risk of violating someone's copyright? What are some the ways to go about getting images to make a site?
Get a camera is the safest bet, and will let you be completely sure about the copyright. Plus you'll get the exact photos you need. You can search photo sites for Public Domain or Creative Commons photos. Most of the images on Wikipedia are can be used at least non-commercially; they force anyone who would upload an image to release it to the public domain so they don't get sued. But that's not true in all cases, so make sure you read the license for each image you're interested in. You can go to a stock house, and purchase rights to images. Obviously, that costs more than free, but you're completely assured of the copyright, model release, and any other legal status of the image. What are you looking for, specifically?
istockphoto.com is one of the best sites that I found. However, if you can only pay via paypal check out this one: http://www.bigstockphoto.com/ They're pretty decent too
www.123rf.com is a great site for royalty free images it has tons of them, you have to buy credits though, but it's worth it