First, know that pages and profiles are different - people usually have profiles, where you have to friend them, and they have to accept the friend request. And some people, groups and companies have pages, where all you have to do is click the like button.
When you go to someone's profile - a person or entity that you have to send a friend request to, and they have to accept it - there is a button at the top of the page that says "Add as a friend" - if you click on that, it will pop up a screen where you can send a friend request.
If you go to a company or person's page, they don't have friend requests - what they have are "like" buttons, also at the top of the page. And you can click on it to like that page. It doesn't go into your friends' list though, pages you like don't show up on your profile for others to see, as far as I know. They will show up in your news feed, though, when the pages have posts.
~suki