Q: Is it really possible to erase a hard drive on a computer I want to sell?

Read What to do before selling or giving away your Mac - Apple Support

Before you sell or give away your computer, in addition to the steps listed in this support article, please take these steps:

1. Run Apple Diagnostics or the Apple Hardware Test. The buyer will do this (or he should), and you don't want to be surprised by the results.

2. Reset the PRAM and the SMC, which might contain personal information.

3. If you set a firmware password, remove it by running Firmware Password Utility in Recovery mode.

4. If you activated FileVault in OS X 10.7 or later, turn it off.

5. If you use Boot Camp, the partition must be deleted.

6. If you created any other data partitions on the internal drive, remove them in Disk Utility.

7. If the machine has an internal hard drive, erase the one remaining data partition with the option to zero out data. An SSD doesn't need to be zeroed.

8. Remove the machine from your list of registered products. If it's still covered by an AppleCare Protection Plan, transfer the coverage to the new owner by following the instructions in the AppleCare Terms and Conditions (under the heading "Transfer of Plan.")

Also note:

You can't legally or practically transfer any software downloaded from the Mac App Store to the new owner of the machine, even if it was free. That includes OS X, so if you upgraded to OS X 10.7 or later, you must reinstall an older OS, either from the installation media, if applicable, or by starting up in Internet Recovery mode (option-command-R at the startup chime.) If you installed from physical media, deliver those to the new owner.

Replacements for the original media can be ordered from Apple.

If the machine shipped with OS X 10.4 or 10.5, then you may be able to install on it from a retail Snow Leopard disc (which you must then transfer to the buyer.) To run Snow Leopard, the machine needs at least 1 GB of memory. The buyer should understand that if he doesn't get the original media from you, he won't get the bundled iLife applications or the Apple Hardware Test.

The new owner will have to redownload any software that came from the App Store, if applicable, including OS X upgrades, under his or her Apple ID. If you ever updated the bundled iLife applications (Garage Band, iMovie, and iPhoto) through the App Store, you can't transfer those either. The buyer will have to purchase them. Note that iPhoto has been discontinued and is no longer available for purchase.

Which Mac model do you have? The link provided by Mr. Eckert is only usable for models that came with Lion or later installed and can use Internet Restore. (It also contains the same information that Mr. Davis has posted or re-stated.) Earlier models will require that you use the Software Restore disc to boot from, erase the drive, then reinstall OS X. Do not install any copy of OS X except Snow Leopard or earlier. Be sure to remove all third-party software that you have purchased and/or downloaded from the App Store including free software. If these conditions fit the computer you have, then here is how to erase and install OS X:

Snow Leopard Erase and Install

1. Insert Snow Leopard DVD into the optical drive and restart the computer.
2. Immediately upon hearing the chime hold down the C key.
3. Release the key when the Apple logo appears and wait for the loading to finish.
4. After the installer loads select your language and click on the Continue  button. When the menu bar appears select Disk Utility from the Utilities menu.  After Disk Utility loads select the out-dented disk entry from the side list (usually, mfgr.'s ID and drive size.)  Click on the Partition tab in the Disk Utility’s right window.  Set the number of  partitions to (1) from the drop down menu. Click on Options button and select GUID, click on OK, set the format type to MacOS Extended, Journaled. Finally, click on the Apply button.
5. After formatting has finished quit Disk Utility.  Continue with the OS X installation and follow the directions.
6. After you reformat your hard drive and reinstall Snow Leopard, the computer restarts to a Welcome screen. To leave the Mac in an OOTB (Out Of The Box) state, don't continue with the setup. Instead, press Command and Q keys to shut down the computer. The Setup Assistant will guide the new owner through the setup process after he/she turns on the computer.

as Linc Davis has suggested under 7 above, erasing the drive with one click off the security erase default to yield "one pass, zero all data" overwrites everything that was on the drive, and is sufficient for all except Nuclear secrets. More passes does not produce any measurable additional security for ordinary use.