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To remove the credit links you need to edit the footer.php file and comment out or delete the relevant line containing the links.

Go ClassiPress Admin => Settings => Advertising
Under "Header Ad (468x60)" you have the option of placing Adsense advertising or publicity own use, you just have to inform the fields "Ad Image URL"...

Ok, the other spot you refer to is the Ad banner.. Also a setting in your ClassiPress admin > Settings, and in there, the "Advertising" tab. If you don't wish to use the ad spot, under "Header Ad...

My apologies, completely I missed the part where you were trying to load the theme onto an actual WordPress.com blog. As has been explained, you need to have WordPress installed on your own host.
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step 1: Go here (or similar) Web Hosting Services, Reseller Hosting, and Dedicated Servers by HostGator and find a server package and a domain name that suits (smallest server package should be fine...