Vibrato is something that should come quite naturally to you - over time. With good vocal technique and with good vocal practice, vibrato should develop as you spend more time on your voice. If you're keen to improve your vibrato, here's what you should be doing:
1. Sing more
The more you sing, the more you get to know your voice. The more you practice and develop your sound, the easier you'll find it to apply techniques like vibrato.
2. Have good breath control
If you have a steady flow of air and even breath control you are going to find it easier for vibrato to come naturally. There's a quick exercise you can try where you breathe in while counting to 3 and then breathe out while counting to 3. Release the same amount of air as you are taking in, keeping it really nice and controlled. You don't have to fill up your lungs and release all of your air. It's just keeping you conscious of what your lungs and diaphragm are doing, and helping you be in control of that breath.
3. Have no tension
This is the biggest killer of the voice. If you can get rid of your tension, whether it's in your tongue, your throat, or your chest you'll find it much easier and a much more natural process to apply vibrato.
4. Keep your jaw still
A relaxed jaw will hep you. Moving your jaw will only give you false vibrato and this is bad technique. It's cheating and not very professional.
5. Don't push your diaphragm
Pushing on your diaphragm with your hands is very uncomfortable and won't help you develop any kind of natural vibrato. It may be tempting to do this to force the sound, but it will benefit you long-term.
Take your time and keep singing, you'll get there! Don't forget to check out Hannah's great lesson on how to sing with vibrato.