With every person you meet in the game, their opinion of you will change depending on what you say during your conversations. Every time you say something they like or respect, you will get usually get +1 like points with them. In order to reach Liked status with people, you must have at least +3 like points with them.
If you plan on getting Ladies' Man, this achievement will come naturally, as the ladies have to at least like you in order to have a chance at romancing them.
If you want to get it a little earlier, you can easily get it before you leave the agency for Saudi Arabia at the very beginning of the game. Make sure you do each training exercise, and say what appeals to each person the most. What to say to each of the four characters is as follows. Also, doing the extra mission each person gives you for scoring well during the training exercise will give you a +1 like point, so don't neglect doing them!
Yancy Westridge: Professional and Aggressive responses is what he admires, as he prefers people straight to the point compared to those that are over-confident about themselves.
Mina Tang: During your time at the Graybox, Professional answers will earn her respect. It's okay to crack a joke or two with her, but don't try to flirt with her. Making fun out of Sean will also make her respect you.
Sean Darcy: Professional answers are key here at first, and an Suave answers after the Graybox work well.
Alan Parker: Aggressive and Professional answers are key with Parker. While he may not always agree with you, he will respect that you are being honest with him.