I forgot my admin password for my mac air

Resetting or changing a password:

For Snow Leopard or earlier: http://support.apple.com/kb/HT1274

For Lion or later: http://support.apple.com/kb/HT6022

This is also useful:

http://www.macworld.co.uk/ipad-iphone/news/?newsid=3463233&olo=email

If it's running Mac OS X 10.6.8 or earlier, insert a Mac OS X install DVD, restart with the Option key held down, click on it, and use the Reset Password utility.

If it's running Mac OS X 10.7 or newer, restart with the Command and R keys held down, open the Terminal, and use the resetpassword command:

https://discussions.apple.com/docs/DOC-4101

OS X 10.7 Lion, 10.8 MountainLion & 10.9 Mavericks

Reset Password using Recovery HD

Boot into Recovery Partition.

Start the computer,then press and hold down command and R keys to start into recovery partition.

When you see the Apple logo, release the keys.

Wait until OS X Utilities window shows up.

Move the mouse to the menubar at the top and click "Utilities", then select "Terminal"

from the drop down.

Terminal window will appear.

Type in resetpassword and press enter on the keyboard.

Leave the Terminal window open.

Reset Password Utility window will open with Macintosh HD selected.

Select the user account from the popup menu box.

Enter a new password.

Reenter the new password for the user.

Enter a hint.

Click the "Save" button.

Click  in the menubar and select Restart.

Log in.

When Keychain dialog box appears, select “Create New Keychain".