Vibrato is a measured change in pitch.  What it boils down to is that you are playing in tune and out of tune very quickly with the result that the notes will have more resonance and more "richness."  Vibrato must not be used to hide poor intonation and students should not start learning vibrato until intonation is very secure.

Following is a "long-range" plan to help you develop a vibrato.  You should spend as much time as necessary to make sure you are comfortable with each step before proceeding to the next step.

Steps 2-6 should be done "guitar style" and under the chin
Steps 7-10 are done first with the heel of the hand in contact with the ribs

1. Extend your arms, palms up, and wave to yourself by flexing your wrist up 90º.  Keep the fingers straight.

2. Place the heel of your hand against the ribs and wave.

3. Lightly touching the 2nd finger to any string, do long, slow slides up and down the fingerboard as far as you can slide without losing contact with the ribs.

4. Gradually shorten slides until they disappear.

5. With the 2nd finger still just touching the string, roll the finger tip forward and back.

6. Gently allow the finger to settle into the string.  Continue the waving motion.

7. Do measured ½ step rolls, 2 per beat, 4 beats per bow.

8. Measured roll with triplets -- 3 movements per beat.

9. Measured rolls with 16th notes -- 4 movements per beat.

10. Gradually speed up and smooth out the rolling motion.

11. Pull back to 1st position and repeat steps 7-10.

12. Repeat the procedure with each finger.

Once the vibrato starts working in a satisfactory manner, you should use it on all long notes and gradually begin to use it on shorter note values until it becomes a normal part of your technique.  Vibrato should be smooth and even and does not need to be especially fast.  It should also not be too wide or narrow.  Let your ears and your teacher guide you toward the best sound.