When following a moving subject carefully by panning the camera, I want to keep the subject steady in the frame and avoid any vertical movement while panning. The goal is to capture the object of the shot with a streaked background while camera is in motion panning and keep the moving subject is sharp.
I do not think it is reasonable to expect you to post in your question the exact ONE specific shooting scenario with all its variables that Michael mentions AND whatever others there may be.
I am assuming you want a basic's understanding of the principles involved to achieve motion blur.
(Some of) The principles involved in knowing how to set your camera to achieve motion blur are.
Using a slow enough shutter speed to achieve the DESIRED amount of motion blur.
Adjusting your other camera setting ( Aperture and ISO ) so that you may use the shutter speed you need to achieve that amount of blur.
How fast the subject is moving and how far away from you the subject is, this determines how fast your camera will be panning and that effects the level of motion blur.
Obviously there are more and it is specific to each scenario. And many previously mentioned variables ( your camera and different lens's ETC. )
I would suggest you practice, first without a moving subject, in a low light situation that allows you to use a slow shutter speed. You could start by setting your camera to SHUTTER PRIORITY MODE and you will need to choose an ISO that will give you the slow shutter speeds needed for this test.
Start at 1/30th of a second and practice at that speed BEFORE moving progressively down through slower shutter speeds. You will want to use nice fluid movement of the camera and ( importantly ) you will need to start panning BEFORE you press the shutter button. Try this at several different panning speeds so you can see the difference in the amount of motion blur for different panning speeds. Now do a series of a shots at successively slower shutter speeds, 1/15, 1/13, 1/10, 1/8 ( as slow as you want but keep it simple. ( you may have to change your ISO if you go to slow. Since you are in SHUTTER PRIORITY MODE your camera will make changes to APERTURE accordingly. With each slower shot you will see a change in the amount of blur and you can change you pan speed to effect that as well. Then try it with a friend as the moving subject on a bike. Practice the fluid movement and releasing the shutter after you start panning.
SPEND A GOOD AMOUNT OF TIME EXPERIMENTING WITH THIS AND YOU WILL GAIN A BETTER GRASP OF WHAT IS HAPPENING.
Next I would suggest that then put you camera in full manual mode so that you have to manually change the shutter speed and aperture yourself so you gain a better grasp of the relationship between the two.
Maintaining a sharp subject can get challenging and each scenario is different. Sometimes a little blur of the subject lends to the sense of motion and overall image.
As stated before you will have to change your technique, speed of pan, settings per each individual shooting situation.
Here are a couple of examples of motion shots i did with Black & White film. Obviously digital gives you instant feedback/gratification.
just have fun!