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.
Free membership

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.
They give a gold membership.

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.
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.

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

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.

Wait so is when you give someone a membership (Diamond or gold) free?
Apparently it was an option early in the site's life but hasn't been for a long time.
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.