When you deal with people, you understand that you are dealing with the creation of your Lord
There is a simple yet profound equation I learned from my sheikh that can help us get a better grasp of what it means to live your life for His Sake.
“When dealing with Allah (swt) remove people from the equation and when dealing with people remove yourself from the equation.”
Every day should be spent aiming to please Allah and not the people, for living a life for His Sake means embodying that in the state of worship you are in and the deeds you put forth and strive for.
When you deal with people, you understand that you are dealing with the creation of your Lord so you give them the best and prefer them over yourself, whether it is through noble manners and character, standing up for justice and the oppressed amongst this world, giving in charity, etc.
You remove any malice, jealousy, apathy, anger, insincerity and other negative emotions for His Sake because you truly recognize the dignity of your created brethren through your Creator.