Well, pitch vibrato should be the base but volume fluctuations on top of it enrich it into a more professional sound.

Most people will, once they have removed excess tension from their singing, develop a natural vibrato, but this isn't true for everyone.
I'd pretty much eliminated vocal tension, but still didn't have a vibrato, but this is fine. It's quite an easy technique to teach yourself, but it takes time.

The most common vibrato is the pitch vibrato, which is usually sung at a rate of between 5 and 7 per second. 6 being the typical rate.

A good place to start is at about 80bpm, doing 2 per beat (For example C,B,C,B for each beat). This should be fairly easy for you. If you're having trouble keeping time, putting your metronome into quaver mode should help.

It's important to stress the change in tone is from the vocal cords, and doesn't come from using your stomach. It shouldn't be pushed.

Now all you need to do is slowly work your way up.
120 is the equivalent of 4 per second, 150 is 5 per second and 180 is 6.

Just keep it easy and relaxed, and when you get to about 140bpm, you will notice it starts to feel a lot easier and more natural.

It will take time, but it's worth it.

When you have this foundation, you can experiment a bit with different vibrato methods, such as "stomach vibrato". In truth, it's more of a tremolo than a vibrato, but can sound very good if done right.
I've found that if learnt before pitch vibrato, it can become a bit of a crutch.
I know it did for me.

Also, Brett Manning does a great vibrato course, but it's a bit pricy.

Good luck, and let us know how you get on

I could do pitch vibrato naturally long before I learnt how to do stomach vibrato. The thing is, pure stomach vibrato sounds a bit ****ty if you ask me. If your voice is free, it typically wants to drop in tone as you drop your support on each "iteration" of stomach vibrato. You can either focus to counter that, or you can exploit it by pushing it even further in that direction. The result is a pitch vibrato with simultaneous tremolo, which sounds much more powerful than just pitch. You can hear many singers doing exactly that, Dickinson being a prime example.

Natural vibrato only comes when your voice is fully relaxed and and can resonate freely. The slightest tension with impede on it on slow it down to a wobble. Don't worry to much about it. Practice your voice placement and your proper jaw opening to create sufficient place for the voice to vibrate and it will come.

Thanks for good advices. Maybe I shouldn't worry about this too much as I still have more critical issues like intonation.

I don't mean to say that I have great vibrato, but to me, it's almost natural. I don't really practice it, it just happens when I sing.. it's a natural reaction when I sustain notes. But when I do the pitch vibrato exercise, it does warm-up it a bit well.