Vibrato is an important tool for the Oboe player and should be incorporated once you have developed a steady sound with a good understanding of tone quality.

To work on vibrato follow these four steps!

Begin by vocalizing “hee hee hee hee” with your voice first. Focus on your core creating the “hee” sound.
Then use your airstream, again focusing on your core to be the reason the “hee” sound is created.
Grab your prepared Oboe reed and play on the reed with that same air pressure and core support.
Finally, play it on your Oboe. Half-hole D is a great note to start on.

DO NOT move your embouchure or your jaw to create vibrato! It is all done by the airstream on Oboe. Follow the examples on the right to hear examples in order.

The only way to get better at Vibrato is to practice it more often! Incorporate Vibrato into your fundamentals routine, just be sure to not neglect working on great, supported tone without vibrato.
A bad tone with vibrato is still a bad tone!