Instead of editing the file by hand there is a dedicated tool (visudo) on linux that is the recommended way for modifying sudo access.
sudo visudo
or, if you want to use e.g. the editor nano, call
sudo EDITOR=nano visudo
Then you have 2 choices:
Easy way
You can turn off the password check for all users in the sudo group. To do that, find the line that starts with
%sudo
and replace it with
%sudo ALL=(ALL) NOPASSWD:ALL
Done.
Alternative way
Alternatively you can turn off the password check for a specific user. Here it is important that you add your new entry at the very last line. Otherwise it might fail, as you can read in man sudoers:
When multiple entries match for a user, they are applied in order. Where there are multiple matches, the last
match is used (which is not necessarily the most specific match).
So, add the following line as the very last line in the file. Do not forget to replace $USER with your username:
$USER ALL=(ALL) NOPASSWD:ALL
You can find your username by calling echo $USER on the command line in case of doubt.