How to run a shell script in background?

Run a command in the background and get no output?

setsid script.sh

Depending on what you are wanting, just add a & to the end of the command

script.sh &
command &

If you are running it in a terminal, and you want to then close the terminal, use nohup or disown

nohup

nohup script.sh &

disown

script &
disown

If that is not what you are after, please be more specific in your question.

sh /tmp/script.sh > /dev/null 2>&1 < /dev/null &

nohup /path/to/your/script.sh > /dev/null 2>&1 &