As a new grandma I received yet more help from my mum (the new great-grandma). To quieten a crying baby especially at night, put a radio playing soft music in the pram or cot - it makes the baby feel less alone and abandoned. In my experience it works brilliantly!
When my son's were little, I used to give them a nice warm bath, their bottle, and then when I laid them down, I would warm the baby oil and give them a full massage. They slept beautifully...teething was the only thing that
interrupted their sleep. For that I took a Q-tip swab, dampened the tip, squeezed a little "Ora-jel For Babies" on it and rubbed it on their gums before meals and bedtime...it really helped.