The number one thing to keep in mind is that your shoulder rest is adjustable! Players of differing size will set up and place the shoulder rest at angles appropriate to their neck and bow arm length.
Though there are many shoulder rests on the market, a good one to start with is the "Kun Collapsible Shoulder Rest," it seems to fit most people and instruments well, and it will last almost forever. Adults will need a full size or 4/4 shoulder rest for a full size 4/4 violin.
Below are some general guidelines to use as a starting point when placing your shoulder rest. The rubber feet of the shoulder rest should grip the edge of the back of the instrument snugly, if a foot is not doing this, try turning the foot around (it is basically a screw with a rubber coating,) so the curved foot hugs the curve of the edge of your instrument.
Make sure your shoulder rest is oriented as seen above, thinner side to the left, thicker side to the right. As one of my students said, the shoulder rest makes the back look like "frowny face."
It is ok for the rest to bend just a bit as you grip the back of the instrument, you'll want it to be snug, but not overly tight.
If your shoulder rest keeps falling off the instrument, try adjusting the distance between the feet to be smaller, or finagle it around to grip the back tighter. Another remedy for a loose shoulder rest is to use a nail file or sand paper to scuff the beige rubber on the feet a bit. ONLY SCUFF UP THE RUBBER FEET OF THE SHOULDER REST! NEVER EVER SAND YOUR VIOLIN!
If you have a longer neck, try unscrewing the feet to increase the distance between the shoulder rest cushion and back of the violin. Be careful to leave enough of the screw in its socket so that it doesn't come out or strip the plastic nut. Another option for a person with a long neck is to increase the length of the shoulder rest feet, here is a link to the Kun Extra Long Foot. You will need one extra long screw to replace the screw that is on the skinny side of the shoulder rest, then move the screw you just replaced to the thicker side (so that your shoulder rest is utilizing both of the longer screws.) It is proper to have the longest screw on the skinny side, and the next to longest screw on the thicker side.
If you have a shorter neck and feel your head is being tilted away from the violin, try screwing in the feet of the shoulder rest a bit.