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The Facebook app icon looks like a white "f" on a dark-blue background. Facebook will open to your News Feed if you're already logged in. If you aren't already logged in, enter your email address (or phone number) and password, then tap Log in. It's at the top of the screen. This should be something you enjoy, such as a music genre or a type of food. You should see the interest appear below the drop-down menu; tap it to search for it. It's in the upper-right side of the screen. Doing so will filter your search to show only pages. You may have to swipe the row of tabs at the top of the screen to the left in order to see Pages. This should be the page you want to like. The "Like" icon is the thumbs-up image to the right of the page. Tapping it adds the page to your interests.
Open Facebook. Tap the search bar. Type in an interest. Tap the interest. Tap the Pages tab. Tap the "Like" icon next to a page.