The first time you started the new computer you created a user account with a username and password set by you. The username is the foldername you see below your account's Home folder in the User's folder at the root of your hard drive. The Home folder's icon looks like this:
Look below the icon for your username. If you don't know your password then see:
Forgot Your Account Password
For Snow Leopard and earlier
For Lion/Mountain Lion
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
When the menubar appears select Terminal from the Utilities menu.
Enter resetpassword at the prompt and press RETURN. Follow
instructions in the dialog window that will appear.
Or see Reset a Mac OS X 10.7 Lion Password and
If you cannot do the above then try this:
1. Boot to Safe Mode by restarting and after the chime press and hold down the COMMAND-S keys until a black screen with white type appears.
2. At the prompt, type the following commands pressing return after each command line:
If you do not receive a "Filesystem OK" message then repeat this command until
you do. If after seven tries you still do not receive a "Filesystem OK" message,
then the system is corrupted and needs to be reinstalled.
mount -uw /
mv local.nidb local.old
shutdown -r now
The second-to-last command above will cause OS X to think that the operating system is newly installed, and when the new owner starts up the computer it will send him/her to the startup wizard where he/she can start a new user without reinstalling.
This last method does not actually change a password. It simply removes the user accounts and lets you create an initial admin account as if the computer were new out of the box.
How to reset the OS X password without a startup CD:
Reboot into Single-user Mode. Enter the following and press RETURN after each command line
1. Type fsck -fy
2. Type mount -uw /
3. Type passwd <username>
I have never tried this method myself.