Sing a single syllable such as "la" or "oh." When you add vibrato, you do so on the vowel sounds that occur in conjunction with notes that you hold for various periods of time. It is the vowels and not the consonants in singing that emphasize the vibrato effect.
Support your voice with your abdominal muscles. This is often referred to as diaphragm singing. Sit or stand with erect posture and contract the muscles in your abdomen gently but firmly as you sing a single tone. This muscle support helps to control air flow through your vocal cords, which in turn helps to create the vibrato sound.
Lower the back portion of your tongue as you hold a note so that your tongue feels as if it were making an "uh" sound. This tongue position also helps the vibrato sound to form. As you are making the "uh" sound, try to relax your throat as much as possible. Pulse your breath slightly as you sing a syllable, and think of the vibrating sound that you want to hear as you do so. If you don't hear the right sound at first, continue trying. Sometimes it takes a few tries to achieve the vibrato effect.
Record yourself singing and compare your voice with the voices of others who have a pleasant vibrato. You don't want your voice to sound identical to someone else's, but you do want to evaluate whether you are producing a pleasant vibrato sound.