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I am trying to be more expressive when I play, so I would like to know what is the proper technique used to do vibrato on the tuba?

When Roy Main was my teacher he had me work on jaw vibrato. I had instinctively developed a throat vibrato but it was too fast and caused other problems. Just close and open your jaw a little bit when sustaining a note, and don't get too focused on the mechanics of it.

I Personally use and recommend to students that they use a jaw vibrato. It's just a slight"chewing" motion and will allow you to move the pitch around. Make sure you work to have a fairly wide vibrato. Otherwise it sounds like you are nervous. Also when you use it, use it bigger than you think you need to as the cheap seats might not be able to translate what you think you are doing into ""expression".

My big rule on this is:
"Using vibrato, is like zipping your pants in public. Use it DISCREETLY - not on everything!"

(1. judicious in one's conduct or speech, esp. with regard to respecting privacy or maintaining silence about something of a delicate nature; prudent; circumspect.
2. showing prudence and circumspection; decorous: a discreet silence.
3. modestly unobtrusive; unostentatious: a discreet, finely wrought gold necklace.)

I don't know how to advise you regarding vibrato technique. But... there certainly is a time a place for everything. Vibrato on certain solo things is OK but leave it at the door in an orchestra or concert band setting. ... ESPECIALLY in a concert band where there might be several tubas in the section.

Ultimately a vibrato is just a controlled repetitive minimal variation in pitch. Frankly I think you're barking up the wrong tree by focusing on it. In my opinion anyway, it's the line that's most important element of lyrical playing.

Concone, Bordogni, arias, Bach cello suites, yada yada. Vocalises. Listen extremely closely to some really good singers. Emulate super-lyrical players - Yo-Yo Ma comes immediately to mind. Listen to Fletcher's recordings. Find the shapes of the phrases, where to stretch, where to emphasize, where not to, and how much. And listen to recordings of yourself doing it.