It couldn’t be much easier. First of all, you install the application using the official Apt repository. You want the repo so security updates and the like are automatically applied alongside your regular unattended upgrades. You are automatically applying security updates, aren’t you?
# Add the release PGP keys:
curl -s https://syncthing.net/release-key.txt | sudo apt-key add -
# Add the "release" channel to your APT sources:
echo "deb http://apt.syncthing.net/ syncthing release" | sudo tee /etc/apt/sources.list.d/syncthing.list
# Update and install syncthing:
sudo apt update
sudo apt install syncthing
Following installation, I’ve seen it suggested to temporarily change the configuration to allow remote web access, but it seems to me that SSH tunneling is much easier to use than changing the configuration every time you might want to enter the settings. Something like this should do. (Update: the manual already mentions it.)
ssh user@hostname -L 8500:localhost:8384
localhost:8500 to access the configuration. You can of course use the same trick to make phpMyAdmin more secure. With that out of the way you can follow the manual for setting up Syncthing as a systemd service.