This is a good question and one we hear a lot! Each mat is different. Some are reversible so it doesn't matter which side is placed on the floor, but you may want to choose a side and stick with it. You could mark the side you put on the floor. That side may become damaged by dust and dirt on the floor and might also become damaged differently than the side you use.
If your mat has a specific side to place on the floor, it's important to follow that guideline. Be sure to look at each side of the mat and then any information that came with it to determine the correct side to place against the floor. That side is usually designed to be more slip-resistant on smooth surfaces than the side you will use.