Think about whether you really want to add vibrato. While you might hear a pleasant vibrato effect in your favorite singers, it's important to keep in mind that those artists evolved their vibrato after years of voice coaching and singing. Forcefully adding vibrato to your singing can have a very unpleasant result, so make sure you consult with a voice coach before altering your singing.
Improve your posture. In singing, posture is critical. Make sure you're standing up straight so you can force the sound out from your diaphragm instead of from your throat. Producing the sound from deep inside you will help give your singing vibrato.
Relax everything. To sing with vibrato you must relax all parts of your body that are involved with the singing. Your throat, neck, head and shoulders should be as loose as possible to achieve the effect. Take a few minutes before singing to relax and stretch all of these areas thoroughly.
Test and gauge your vibrato as you go. Lie down on your back and breathe normally, with your hand resting gently on your stomach to feel your breathing. Pick a note that is comfortable to you and emit that note at a comfortable pitch. As you do so, pay attention to the relationship between the level of vibrato and the tension of your abdominal muscles. If the muscles are too tight, the vibrato will be squashed, so try a lower pitch, relax further and record yourself to see how you progress.