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1) I recently joined Costco. Their payment methods are Debit Card, Cash or American Express. I opened an American Express Green Card which ultimately I decided I will not use. If I cancel this credit card will it effect my credit score?
2) I made a purchase on 9/17/13 at Best Buy. The sales agent told me about a financing deal with no interest if the balance is paid off in 6 months, so I signed up for a Best Buy credit card. My current balance as of 9/27/13 is $551.97 which I intend to pay off in full prior to the due date which is 10/13/13. The credit limit on this card is $4,000. I have not further use for this crdit card and intend to cancel it. Will this effect my credit score?
Cancelling won't help or hurt your FICO provided your utilization on your other CCs are low.
Welcome to the forum.
Closing your cards will only effect your score if it raises your utilization. Are these the only 2 credit cards that you have? If they are, you may want to leave them open to show a good history of revolving credit so if/when you apply for another card in the future, you have a better chance at approval and a higher initial CL.
Ultimately it is up to you whether you want to keep them open or close them. If you feel you are not a risk to charge up amounts that you can't pay then they are not hurting you.
Instead of asking "Will X affect my credit score?" every time, read up on the factors that affect credit scoring. You've already taken whatever hits to AAoA and to inquiries from opening the cards. The biggest immediate effect from closing a card is the impact on utilization (though it's not quite the same for charge cards, IIRC) and you can do the math to determine your utilization before and after. You should really consider these things before applying for anything versus after you think you want to close an account. You can also reference this sticky in the Credit Cards subforum:
http://ficoforums.myfico.com/t5/Credit-Cards/Closing-Credit-Cards/td-p/347190