In the United States you just start using the trademark, and if you're the first to do so, you own it. Often people refer to "trademarking" or registering their trademark. You don't have to register in order to obtain ownership over a trademark, but it helps.
Requirements of Trademark
Not all words or designs can function as a trademark. For instance, certain words or symbols are banned from trademark protection, such as immoral/scandelous trademarks or the names of living US Presidents. One of the most common reasons a word fails the requirements to become a trademark is that it is generic. Generic terms are the names/labels of the product or good itself. It is therefore deemed incapable of serving to identify source, which is the entire function of a trademark.
Among the greatest advantages of owning a federal trademark registration is that you may deter others from using your trademark. This avoids expensive enforcement & litigation down the road. What's more, a registration will make it easier to enforce your rights down the road for numerous tangible and intangible reasons.