You have the option of rewarding Inspiration for acting their flaws, bonds, etc. (p. 240-241, DMG).
There are some things you can do that aren't system dependent, including:
- Lead by example.
When they talk to NPC's, speak in character. You can watch a few videos of experienced GM's running an encounter. - Have people describe their actions beyond "I roll to do ...yay it worked".
A check isn't just a random success or failure, its designed to model something in the game world.
If you are persuading somebody, you have to talk - have them act it out, just like you (since you're setting an example) what they say.
- Example:
Oh no! The factory manager is about to jump into an industrial mincer! You arrive just as he has climbed the gantry above the mincer.
You(in character): "Don't come any closer, I'll do it!"
Have the players act out any check they make that involves speaking. (persuasion, perception, intimidation)
Do they try to break the machine? If the check succeeds, have them describe what they do. This lets them show how their character thinks and does stuff, even if its just the barbarian and he is hitting the machine with a mallet.