There is no "SkyTeam card". Skyteam is an alliance of 19 member airlines, and it doesn't operate a single Skyteam frequent flier programme. The member airlines operate their own programmes, and there is a certain degree of co-ordination between the programmes - or rather, the various status levels within each individual programme are also matched to a certain SkyTeam status level, and benefits are accorded to fliers on the basis of this level when they fly with a Skyteam airline that is not their "normal" airline. But there is no such thing as a "Skyteam frequent flier programme" or a "Skyteam card".
Most of the individual airlines in the Skyteam alliance operate their own, individual frequent flier programme. (Some - such as Air France, KLM, Kenya Airways, Air Europa and TAROM - share a single programme between them). You must pick one of the frequent flier programmes of any one of the member airlines, and join that programme via that airline (see the airline's website for details on how to sign up to their programme). Subject to the normal earning rules, you can then earn miles in whichever programme you joined whenever you fly on any of the Skyteam airlines. When you have flown enough to achieve any of the various levels of status within that programme, you will have certain privileges that will be accorded to you by any of the Skyteam airlines whenever you fly on any of those Skyteam airlines.
You can see the list of all member airlines
here. Click on each airline name to find out more about their frequent flier programme. In general, it is advisable to join the frequent flier programme of the airline which you will use most frequently. But there is no single answer to the question - Which programme should I join? - the answer will be different for everyone. To read up more and to help you come to a decision, see the following recent thread, and follow the links posted therein:
http://www.flyertalk.com/forum/skyte...gram-best.html
But note that most airlines will not just immediately send you a card when you enrol - in fact, most require that you actually do a certain amount of flying before they send you a card: see the following recent thread:
http://www.flyertalk.com/forum/skyte...d-joining.html
Particularly when you are starting off (and therefore have no status, and are not entitled to "perks" such as lounge access, check-in at business class desks, etc)
you have no need for a card at all. As long as you quote your membership number at the time of booking your flights, and ensure that the number appears on all your boarding passes (and check with the agent at check-in if this is not the case), there is no requirement to actually have a card.