They say platnium and diamond members can give free membership yearly. How does one do that? I have a friend who can't figure that out.

That is a bit of a misnomer since chess.com is free to join and you get a whole bunch of great free stuff. They're probably talking about certain things that free members have limited access to without the "paid" memberships.

They give a gold membership.

yes, i was wondering how. Do they have an option of typing a members name and boom. membership?

See here.

can you be a free member forever or does your account expire?

You can be a free member forever--your account never expires.

if someone gifted membership to you, can you be gold forever..?

apparently not.

how long then? and how often can someone gift memberships

The gift gold membership is for one year. Go to "Account" to find any premium membership you may have to give away. You just type in the nickname and boom! Yes it works, yes I did it.

If no joy there, then try this:

http://support.chess.com/index.php?_m=tickets&_a=submit

Also note that this is no longer possible for new platinum/diamond members.

you can't gift membership anymore?

You can buy a gift membership still, but you no longer receive a free one with Platinum or Diamond memberships.