I suggest singing any sort of warm-up for the voice. a lot.
Then one day, your vibrato will magically appear, and there will be much fanfare.
Really.
Don't force vibrato. It makes you sound stupid. Ok, so maybe not stupid isn't the best word for it, but you will be looked down upon. Probably.
It's silly, don't do it.
That in no way means you should be afraid of your vibrato sounding fake, because it probably doesn't. Forced vibrato is pretty easy to spot because it sounds ridiculous, so if you're worried, listen to yourself.
On the topic actually singing with vibrato, I regret that I can't really give you some sort of definitive technique. If there were, we all would be forcing vibrato. Keep in mind, vibrato is very different from one person to the next. I'm going to emphasize the word very. There is no "trick" to developing a vibrato. I would also like to note that vibrato has nothing to do with the stomach ( I mention this because it seems some people are under the impression that vibrato comes from the stomach).
I would tell you to sing until your vocal chord's bleed, but that's decidedly a bad thing and probably counterproductive. Sing a lot. Have good breath support as always. Vibrato should be very natural. You really don't have to think about it. I challenge you not to do so for a while.
Its really just a matter of getting used to your own voice and what it wants to do.
At least that's what conclusion I have come to in my infinite 16 year old wisdom.