If you can't invite somebody you can accept random challenges by clicking plus icon top right corner ....
Hosting a Table
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The problem I have is every time I click on "Play Live" someone is already on my table and the game has started. How do I create a table and then invite who I want?
Do I have to be a paid member to create a table?
You don't need to be a premium member. :) It sounds like you are seeing the top games when you enter live chess. You should be able to close out that game and see a blank table where you can challeng others.
If you don't wish to see the top games when you enter live chess, you can disable them in your settings.
(Shown here: http://i.imgur.com/dyiACQz.png )
For more help on challenging others in live chess, please see this page:
https://support.chess.com/customer/portal/articles/1444887
Have fun! 
I am new to this site even though I signed up a while back. Is there a way I can set up a table and then invite someone to play instead of someone automatically starting a game with me? I may be overlooking the obvious but everytime I try to play no options are available when it comes to inviting someone. Thanks for any help.