It is generally discouraged to allow SUDO to work without a password, that said, if you are the only one using the machine and have to use SUDO often then it can make life a lot easier.
To enable SUDO without the need to re-enter your own password, you need to first run the sudoers file editor, do this by running visudo:
This will normally take you into VI to edit the sudoers file. If you'd rather use Nano or a different editor then run visudo like this instead:
The reason visudo is recommended over editing the /etc/sudoers file manually is because visudo verifies the file after you have edited it to make sure it is still valid and generally makes sense.
Now, once inside the sudoers file you simply need to add one line to enable your user to firstly use sudo and more importantly, use sudo without a password:
myuser ALL=(ALL) NOPASSWD: ALL
Replacing 'myuser' with your own username. Now save the file. Visudo will tell you if there are any issues. If all is well then you'll be sat back at the terminal and Sudo will now be ready to use, without a password.