During the installation process, you are asked for your MySQL login information. The best place to start would be to make sure this information is correct. If so, then you will need to make sure you have the proper priveledges set for the user you are logging in with. If your host does not allow you to set priveledges, then you will have to contact them.
phpMyAdmin
Begin by selecting the Priveledges tab and click on Add New User. From there, set the information you are using to login (username, password, host, etc.), select all permissions and save. You should now be able to complete your installation.

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