In daily life, there’s pretty much three kinds of frictional forces that you’re likely to encounter if you classify them by how much they are affected by speed. We’ll not worry about the direction of those forces since for our purposes it’s good enough to say that friction acts in the direction opposite the motion. So we can drop the vector notation.
The first one is those frictional forces not affected by speed, like sliding friction. As a good first approximation, this is given by
The frictional force is just equal to some constant depending of what material are producing the friction times the force perpendicular to the surface which your object is sliding across. Heavier objects mean more frictional force. It’s easier to slide a book across the floor than it is to slide a piano across the floor. But it really doesn’t matter how fast you do the pushing, the force per distance stays the same.
The second is viscous resistance. Dip a smooth stick into the still waters of a pond and very slowly and smoothly move it around. You’ll feel a force resisting the motion which is proportional to the speed of the stick.
Also very easy. You have some constant b which depends on the size and shape of the object and the properties of the liquid. You have the velocity. Multiply them together and you get the force.
Now why do you have to move the stick very slowly and smoothly? Because if you start moving it too quickly you’ll get turbulence. What’s turbulence? Basically, it’s lack of smoothness in the fluid flow. Like this picture, from Wikipedia:
Once you get turbulent flow, the frictional force starts to be proportional to the square of your velocity.
The constants are unimportant, the v2 is the issue. Go twice as fast, and you have to put in four times the work. While aerodynamic drag is definitely not the only thing sapping a car’s forward progress, at highway speeds it’s a very significant effect. A car traveling at a slightly over the limit speed of 75 mph will experience about 1.15 times the drag as a car traveling at the speed limit of 70 mph. While 60 mph is hair-tearingly slow compared to 75 mph, it reduces drag by better than a factor of 50%. Now you definitely shouldn’t drive unsafely slow, but even cutting your speed to 70 from whatever slightly-over speed you usually prefer can save you considerable gas at the cost of only a tiny bit of extra travel time.