When you break it all down, all of us instrumentalists have only one goal: to sound as natural as singers. They are the best example we have of lots of things, including phrasing and vibrato.
Developing a really great vibrato (and identifying when and how to use it) is a very important thing for an instrumentalist.
(Note: This is not to say that any musician should ultimately develop only one vibrato. Variations in vibrato give us way more tools with which to tell our musical stories.)
But where do you start?
My advice would be to find three examples that speak to you of a singer using a vibrato. Then analyze them for the following:
- The speed of the vibrato
- The width of the vibrato
- When vibrato is used and when it isn't
Take one of the examples and try to copy the three above things on just one note in your middle register at a medium dynamic. The key (always!) is to record yourself and immediately listen to it.
Once you have a version that sounds somewhat similar to the example you are trying to mimic, move on to the next example, and finally the third.
This exercise will at least give you a starting point for developing a vibrato that can help you to convey your musical ideas.
Bottom line: Always start with singers.