When setting up a hard drive or even after using one for a while, sometimes it is useful to partition it so sections of its space can be used for different purposes. These purposes can be to set up a multiboot environment, separating system files from user files, or for segmenting used data from scratch and backup disks. For instance, if you use a drive to back files up, it may be beneficial to create one large partition for Time Machine, and have a second partition be used for manual backups since Time Machine will eventually use most of the space on its partition.
There are two built-in ways to partition drives in OS X. The first is to use the Boot Camp Assistant, but this is only used for setting up Windows on the newly created partition. If you have other purposes for your partition besides running Windows, or wish to create more custom partitioning schemes, then your best bet is to use Disk Utility.
With Disk Utility open, you will see a list of available disk devices in the list to the left. Under each disk will be a list of volumes (formatted partitions) that the system recognizes on that disk. To partition the disk, select the device itself (not any of the volumes) and you will see a "Partition" tab appear as an option to the right of the list. Select this partition and you will be presented with the options for partitioning your drive.
To the left side in the partition tab you will see a Volume Scheme, under which you will have options to add partitions either via the partition menu or by using the graphical volume map. Setting a partition scheme with the partition menu or partition type with the "Options..." button will rewrite the entire partition table, which cannot be done on boot drives; however, you can modify the current partition scheme on a boot device. To do this, click the plus button at the bottom of the volume scheme and the system will create a new partition for you (click again to add more partitions, or select one and click the minus button to delete it).
With the desired number of partitions set up, size them either by moving the dividing bar between them, or more accurately by selecting one and setting the size in the Volume Information section. When the sizes for each volume are set, name the new volumes, specify a format, and then click the "Apply" button. Disk Utility will show a summary of the changes before continuing to partition the drive.
Keep in mind that modifying the partition table always carries a risk of data loss, so be sure to fully back up the data on your drive before making these changes. Additionally, if you plan on removing a partition, then all the data on it will be deleted. Disk Utility does not provide the option to merge two partitions so the safest route is to copy all the data from the smallest partition to another drive, delete the undesired partition and resize the remaining partitions accordingly, and then copy your data back.