Have been singing since I can remember
Lessons since I was 9
Did a music degree at Cardiff Uni - voice was my main instrument.
Been singing now for 22 years.
There's some great bits of advice on here particularly from *Coldandsad
Vibrato comes in time. Though some people never develop that and sometimes it's lovely to have a pure voice that doesn't have vibrato.
Do not sing from your chest.
The majority of the work will come from your diaphragm, breathing, mouth, tongue and vocal cords.
If you're struggling to find your voice, try and sing pieces you haven't heard anyone else sing. For example, if you sing songs by Adele, you'll most likely try to imitate her sounds. If you pick a song you haven't heard someone else sing, you might have a bit more luck.
Exercises you can do are scales, diction exercises (repeat the same consonant 3 times all the way through alphabet with as much clarity as you can, almost over the top) and breathing exercises.
With regards to hurting your voice, practise should only ever be at like 80% effort. Never go full throttle. And make sure you are using your diaphragm for power and opening your mouth as wide as possible for the words you are singing.
My teacher used to tell me to lift the back of my throat to sing and I had no idea what she was on about until I went to Birmingham Conservatoire for an interview. The gentleman who met me called it the soft palette. When you yawn, the soft palette at the back and top of your mouth lifts up. When singing you need to try replicate this as much as possible.
For the early days, I would just do exercises, pick some neutral songs to sing to find your own voice, maybe practise holding your breath to exercise and expand your lung capacity. The rest will come with tutoring and time.
Also, please bear in mind that the voice is a muscle. It will take time to build it and support it. Your voice will grow with time.