Hi! I'm pseudolatino, from Catalunya, Spain.

When you use vibrato you dont need to shake your violin. Just quickly push up and down on the string with different pressures.

well, i taught myself how to vibrato and it took like a week so be patient! lol-- you should practice it with scales instead of songs cuz that'll be difficult (until you start to get it)
there are three kinds of vibrato: arm(easiest), wrist(what i do) and finger(most difficult)
start with moving your arm back and forth slowly and make sure your finger stays on the same not but not exactly the same place because vibrato is actually a fast repetition of two notes right next to eachother. as you get better you'll use your wrist more, get faster and be able to do it with your pinky finger! hope this helped!

oh yea and TRY TO KEEP THE VIOLIN IN PLACE!! lol