1. My first child couldn't be calmed easily, although I found a song that somehow worked. [0]
2. Second child could be soothed by slowly rubbing from his temple down past his eye to his cheek.
3. Third child hated that, but loved having her forehead rubbed slowly in a horizontal manner.
4. Fourth child just wanted a firm pressure on the top of his head (e.g., a palm, he'd also burrow up into your armpit for comfort sometimes, which was awkward when I hadn't showered that day)
5. Fifth child didn't need any of the above, just lots of hugs and kisses at bed time. Bless her.
The only generally applicable rules I found are:
* Sleeping on your chest when young where they can hear your heartbeart (I found it works best with Dad when breastfeeding, as the smell of Mom's milk tended to stir them up for a feed, even if they're struggling with wind and not able to feed) can be very calming. Ideally done skin to skin.
* Slow rocking while making a continuous "sssshhh" noise often helped - the fact I'd become a human white noise generator amused me.
* Patiently, calmly, love them. It's most important to do this when it's hardest to love them. Knowing that they can be total assholes and you'll still love them is what grows secure kids.
* Ask for help when you're struggling! A lot of your friends and family are probably desperate to help you, but they don't want to appear condescending, or to intrude. So give them permission, explicitly invite them to help, and your sanity will return, which will make you a much better parent for baby.
That's it. That's all my parenting advice after five babies.