You can apply for a trademark with an intellectual property office of the country where you are seeking protection. Practically speaking, you will submit a trademark application which the IP office will then assess.
Depending on the country of your choice, you might be able to apply yourself or be required to have a legal representative. Usually, you can apply yourself if you are a citizen of the given country, but some countries also allow self-filing in other cases, such as your company having headquarters there.
When applying, you will have to provide ownership details (of you or your company, depending on who the owner will be), select trademark type (wordmark, figurative mark, sound mark, etc.), provide a logo if you are applying for a figurative mark, and provide a list of classes of goods or services you want the protection for.
You can read more about how to prepare the application and what questions should you be able to answer before applying in our article on the Application process.