A lot of people focuses on external details of a different culture. Things like the funny clothes, different manners, and different customs. That is hard to do because it involves memorizing details. If you try to simplify things then you wind up with caricatures which can be also unsatisfying.
My opinion is that the heart of having different cultures is that they have different motivations. That what you need to focus on. The High Elves have different concerns from the Grey Elves, who have different concerns than the Mountain Dwarves, who have different concerns from the humans of Imperial Ghinor and so on.
The way I implement this in the backgrounds for player character. Before each campaign I sit down with each player and together we work up a background for their character. The player throws out some ideas and I give her some choices as to how they would work in my setting. We go back and forth until we have a background that both of us are happy with.
The key element is in the choices you give the player. I know the cultures and societies of my setting in detail, the player generally doesn't. The choices are tailored to reflect the origins of the characters. An elf focused on revenge for orcs killing his family is going to look different than a dwarf with the same issues or a human. All of this comes out when developing the background.
Also this processes teaches the player how you implement different cultures. Even they don't pick certain options you give them just the fact you presented them and talked about them teaches the players how that culture works.
Ultimately the reason you put work into this is that because cultures have different motivations they may come in to conflict when they conflict. This conflict is fodder for an adventure which is the heart of tabletop roleplaying games.
I am not too enamored of mechanical rewards for roleplaying. I find that mechanics for roleplaying often lead to unrealistic results as players game the mechanics. The best one I seen are traits systems, like in Pendragon. In effect, they are short concise descriptions of the longer verbal descriptions I talk about above. They help players remember what important to their character.