How do you apply for a trademark and what rights does it exactly give you?

If you're in the United States, trademarks are issued by the US Patent & Trademark Office. They have an application form available online which is appears simple, but is not.

The application process takes a minimum of six to seven months, and can take in excess of a year, depending on the complexitiy of the application and the issues it raises.

The rights a trademark gives you are the right to exclusive use of your mark in the international classes of trademark in which it is issued. Registering your trademark is a prerequisite to any legal attempt to enforce or protect your mark in the federal court system.

You can read about it here. It's to much info to post here.