You can request a card from a Club Log user provided they have switched on OQRS on their account, and uploaded the QSOs in question. 

Start here:

Enter the log to search, and your own callsign. Then click "Show Contacts".

Make sure you are in the log. Remember, the DX station might not have uploaded their log, or they might not be using OQRS. If the other station has not enabled OQRS you will not see any option to request a card - even if you are in the log.

If they are, you can proceed to request a card:

Now, follow the instructions to the checkout.