A (very new) member has a MacBook Air from a relation, but doesn't know the old password to allow her to add new programs etc. - how can she change it?
Probably your contact will enjoy best results if she erases her MacBook Air drive using Disk Utility and then installs whatever version of OSX it will run (probably Mavericks — which is free). She can then download Apple stuff from the App store as required. If the relation is willing to give her the Admin password, that would be another matter -- as Lionel rightly points out.
The days of the grey install and start-up DVDs were maybe over when the MacBook Air was produced and it never had an optical drive but used the the hitch-hiking arrangement Apple came up with. An external DVD drive with a USB connection might not be as useful as it seems in these circumstances.
She will need to use the emergency partition (if available) or an independent USB drive with a suitable OS installed on it. Access these by holding down the Option key (Alt) at startup to show the available startup options.
This method means she won’t keep stumbling over her relation’s Keychains, User folders and other setup items such as Mail, etc., and, frankly, it is probably the courteous thing to do. I am happy to discuss the hard- and software options with her and help her erase and install on a clean drive.
(There are other ways to replace the password, but the fact that one can, may not mean that one should...)
Michael Corgan 