Read the quote carefully again, It starts with give respect, rather than demanding it first. You may ask, why can't the other person start it first, Well, I'll say that if you want to be good, wanna be appreciated and liked, then you have to do it first.
The hardest part of it is when you deal with negative people. In the first place, they just cannot give respect but expect it enormously. So what you have to do here is oppose to them respectfully so that you are able to convey your message and they too get a slight tinge of realization. An added advantage is that this trick will never ditch, it will always work, I've had enough experience on this.
Being good and keeping your attitude under check will always help. When you do this consistently, people will start to respect you, that's when you've completely accomplished it. People will start liking anything you do, will start to consider anything you do or say at a deeper level.
But it doesn't mean that once you start getting respect, you can let your attitude go haywire. You should always respect others and do it for every moment from now on. It's not at all difficult, you just have to make a deep cut in your ego, which is great and then you'll see a world of change in you and around you. Good luck with it and start now, it's never to late! Be happy!