Here are instructions on how to copy a DVD.

Important Note: Using Disk Utility will NOT work for all DVDs. Most commercial DVDs intentionally have copy-protection mechanisms in place to prevent disk duplication. This method should work fine for DVDs you made using iDVD, for example.

1. Open Disk Utility.
2. Insert your DVD into your Mac.
3. Wait until the DVD shows up in the Disk Utility window, then click on it once to select it.
4. Go to the File menu, select New, and from it’s sub-menu select New Disk Image from <DVD name>.
5. In the Save As dialog box that appears either accept the proposed name or type in your preferred name. Then select a folder, like the Desktop, where the disk image will be saved. Click the Save button.
6. Wait for the disk image to be created. Depending upon the speed of your computer this can easily take 30-60 minutes or more.

Once the disk image has been created you can follow these steps to burn a new DVD copy.

• Open Disk Utility.
• Go to the Images menu and select Burn.
• In the “Select Image to Burn” window select the disk image which you created previously, then click the Burn button.
• Insert a blank DVD-R disk and wait for the image to be burned onto this blank disk. This process can also easily take 30-60 minutes or more.

[Update: 3/29/19]

With the release of Mac OS X 10.11 (El Capitan), Disk Utility no longer includes the Burn command.  You can burn a disk image from the Finder, however using the following steps:

1.  Control-click the disc image file
2.  Choose “Burn Disc Image [disc name] to Disc” from the shortcut menu, then follow the instructions

More details can be found here:

Apple Mac OS User Guide

You can also use the free Burn app.