Scroll down your profile page and on the right see recommendations of who to follow. Click on the button next to their image and you'll then be 'following' them. This means that as well as all your activities on your timeline, you will also see all their activities.
Alternatively, do a search for the user you want to follow and when found, you'll be able to follow them from their profile page.
Note that by default, you will automatically follow any clicked profiles. However, they (and you) have the option to approve or reject any potential followers. This is configured as part of your profile/account privacy settings (see below).