I recently tried my hand at panning - a technique to cause motion blur of the background while keeping the foreground (which is moving) in focus. I looked around for some detailed information, but couldn't find much until I submitted a post to Reddit for advice (link at the bottom). I'd like to summarise the responses there (credit at the bottom) as well as adding some of my own thoughts.
Panning adds a sense of motion to the picture. If you freeze a car, all the energy and story of the scene are lost.
You can take panning shots in any light, and with any lens. You don't need an expensive prime / f2.8 zoom as you're leaving the shutter open.
It's a whole lot of fun!
Practice makes perfect
The first time you do this, you're going to miss most of the shots. I had a 5-10% rate of nailing the focus. Hopefully with some of the tips below you can improve on this.
Background is important, but not nearly as much as with stills. You're going to blur the background, so you don't need to compose perfectly. A higher contrast background is going to provide a sense of faster movement, but a lower contrast background will blur at much shorter shutter lengths (you don't need much movement to blur grass or road).
When holding the camera, you need to minimise any unwanted movements (eg: vertical shake). You can do this by setting a firm base with feet apart. Hold your elbows in against your chest tightly, and do all of the movement with your hips. You're going to start by swivelling towards where the cars are coming from, so that when they pass you at the point you want to take your picture you're straight on and at your most stable/smooth.
Positioning is key. While it is possible to pan with cars coming towards you, it's a very specialist effect and hard to pull off reliably. For the easiest shot, you want the car travelling perpendicular to where you're standing. Not so close that you're having to twist a lot, nor so far away that you need to use a long telephoto which could introduce vertical shake.
You can vary a lot of the settings based on what you're trying to achieve, but panning means you need to stop and think about all of the settings that you normally work with, and consider what other effects they might have.
The one subject that gets discussed a lot is shutter speed. The lower you set this (eg: 1/30-1/50), the more the background will blur, and the faster the car will look. The flipside of this is that you'll need to track the car much more carefully to achieve a good focus - I had a 4-7% success rate with 1/30 on my first shoot. Conversely, if you set your shutter speed faster (1/100-1/150) then you're going to have far more images with the subject in focus, but the background will show less blur. This can be useful if the background has relatively low contrast (eg: grass). You're going to get blurring from the wheels anyway, so there will always be motion, even at these higher speeds. I'd suggest taking a range of shots at different shutter speeds - this way you'll likely have some that you focussed well, and will learn which setting you want to try for in the future.
Focussing can be tricky - do you rely on the camera to do it on the fly, or should you focus manually? This subject was explained really well in a post by indyphil (an automotive photographer) on reddit. Single point focus is the best mode to use with autofocus, but there is a more important consideration. If your camera has the option, you need to select continual autofocus vs once-per-shutter press. This means that the camera should re-focus as the car comes towards you/away from you. If you don't have that option, or you don't think your autofocus will keep up, another trick is to use autofocus on the point of the track where you plan to take your picture, and then switching to manual focus to actually track & take your shots, that way when the car is at the right point, you know it will be in focus.