How can we implement credit card transactions in Yii?
Your question is not that detailed of what you have tried or you are asking about API or something. What i can say is
Stripe has a PHP library to accept credit cards without needing a merchant account.
If you need something quick and dirty, you can just use PayPal's "Buy" buttons and drop them on your pages. These will take people off-site to PayPal where they can pay with a PayPal account or a credit card. This is free and super easy to implement.
If you want something a bit nicer where people pay on-site with their credit card, then you would want to look into one of those 3rd part payment providers.
Basic procedure is something like PayPal works like