Perform some breathing exercises to prepare yourself for singing vibrato. Take a deep breath of air in, imagining a large balloon inside you filling up. Press your teeth to your tongue and breathe out, as if a small amount of air was escaping from the balloon. Make an "sss" sound and keep the breath at the same volume throughout. Hold this steady for as long as possible to teach your singing muscles control. Keep the sound stable and stop when you're out of breath. Practice doing the sound louder and in several short bursts to further gain control.
Stretch your body out to prepare yourself for singing. Stay relaxed and maintain a good posture. Take a deep breath in and then sing "ahh" in the same steady, relaxed way you did the breathing exercise in. Keep practicing and the natural oscillation of your voice will create the fluctuation required to produce vibrato.
Lie down on your back and place your hand on top of your belly button. Breathe deeply so that you can see your hand rising and falling. Sing a comfortably-pitched "ahh" note and listen for vibrato. If the note doesn't fluctuate, pay attention to what your stomach muscles are doing. People often force the note with their stomach muscles, and this can actually be a hindrance to vibrato. Sing gradually quieter and quieter until you hear vibrato in your voice. Note how your muscles move when this happens, and gradually working to producing the same effect at louder volumes.
Manually fluctuate your tone if none of the above is effective. Sing a C note and then consciously shift it up to C sharp. Use a piano to assist you in making such a minor adjustment in pitch if required. Revert back to C and then repeat the process. Although this will seem unnatural and slow at first, with time it can develop into a vibrato-style fluctuation in pitch. Continue attempting to achieve "natural" vibrato if you are using this method, because it is good practice for overall vocal control.