I am creating application for MAC using cocoa framework, I would like to know how and what are the ways i can connect to MySql database using cocoa framework.
Short answer: You can't, at least not directly.
The Cocoa Framework doesn't have a database driver, generic or otherwise (CoreData notwithstanding). In order to connect to a mysql database you need to use the aptly named libmysqlclient
. This library is not included with Xcode, and as such will have to be downloaded (and probably built) separately: You can get it from here.
You'll probably have to distribute the library with your application, license issues might result.
Edit: It seems as if a library for connecting to the mysql database should be installed together with a MySQL server install. If the application will only need to run on machines where MySQL is installed, you might get away with linking to this.
You might want to look into http://www.sequelpro.com/docs/Source_Code. They seem to have resurrected the original MySQL-Cocoa code and it seems to be under active development. The other option is the commercial MacSQL Framework.
Edit: You might also want to look at the following tutorial. It is a great introduction in using the libmysqlclient and even provides a sample Xcode project.