visudo is a command provided for editing the sudoers file in a safe way. To quote its manual page:
visudo edits the sudoers file in a safe fashion, analogous to vipw(8).
visudo locks the sudoers file against multiple simultaneous edits,
provides basic sanity checks, and checks for parse errors.
/etc/sudoers.tmp file is lock file used by
visudo. Your changes are written to this temporary file so that
visudo can carry out its checks. If everything checks out okay, the main
/etc/sudoers file will be modified accordingly.
So when you run
sudo visudo, a command line editor pops up so that you can edit the file. In your case, this editor appears to be GNU
nano. In nano, you can navigate to the bottom of the file using arrow keys (or the Page Down key), and then paste the lines you want to include. Once your changes are done, you can exit the editor with Ctrl + X and choose the 'Y' option to save the file (you'll be asked to confirm the filename - just hit Enter).
Your sudoers file should now be updated. You can use a pager like
less to read the file and confirm that for yourself (the command to do that is
sudo less /etc/sudoers).