I have a machine running Debian stable, and I'd like to update the stock kernel to the latest kernel available in the backports repository. There are many kernel-related packages and virtual packages--what is the right way to do this and get the appropriate packages upgraded?
Use a meta package (e.g.
linux-image-2.6-686), depending on which you want to use. This is so that if the real package name changes (which is very often), you won't lag behind. To determine which meta package to use, have a look at the name of the kernel package you are running. Also, do read the package descriptions of the meta packages that seem like the right ones, just to make sure.
apt-get -t squeeze-backports install linux-image-2.6-686
Once you have done that, there is no need to keep re-running the command to check if a newer package is available because your normal
apt-get update && apt-get upgrade will do the check for you and upgrade it. Note that this behavior is new (since Squeeze), and in the older days, you had to APT pinning.