There is already a hidden file in your home directory called .bash_history which you can print it. One observation here: this file, in a default configuration, doesn't contain the commands used in your current opened terminal session. So, close the terminal before to print it.
But if you want to save the terminal history in another file, then you can use the following command (this new file will contain also and the commands used in your currently opened terminal session):
history > history_for_print.txt
A new file called history_for_print.txt will be created in your currently working directory containing your last used commands (by default HISTSIZE=1000 and HISTFILESIZE=2000, but you can change these values in your ~/.bashrc file).