The #kernelnewbies irc channel gets visited regularly by people who would like to get a job as a kernel hacker, but are not sure how to get such a job. There are entry-level kernel jobs, but most often you need some experience working with Linux.
First, make sure you actually want to have a job as a Linux kernel developer. Read this page to get an idea of what it's like to be a kernel developer.
To get a job in Linux, you'll need to be experienced in using Linux. Try out a Linux distribution on your home machine(s) and just play around with it. If you're a student, use Linux machines at your university, or help out with maintaining the university Linux/Unix labs. Knowing command line basics will help you get a job. Most importantly, you'll need to know how to build and install your own kernel.
It can help (but isn't necessary) to have background as a Linux system admin. In that job, you get to fix problems by trying out new software, finding and fixing bugs and trying out new features (eg. LVM) when they become available. This makes you familiar with many aspects of the Linux kernel and other parts of the Linux system. More important still, it gives you some of the problem solving skills, and patience, needed to be a kernel hacker.
It's also helpful if you can show you have experience reporting Linux kernel bugs and testing fixes. One way to help out is to build the latest kernel, test it, and report any issues. That way, you'll get a feel for how kernel developers triage bugs, along with what sort of information they need to debug the system.
Try to stay objective about what the cause of the bug is when you report a bug. Report all information and debugging you did first, without trying to attribute what the cause is. Then state what you think the problem is, and possibly post a patch. That way you won't bias the maintainer from seeing what the real root cause of the bug is.
Kernel development experience
When applying for entry-level Linux kernel jobs, you will get major bonus points if one of your patches has been accepted into the mainline kernel. However, note that simply getting spelling fix patches in the kernel isn't enough. Your potential employer will be looking at the Linux kernel git history, and they will be able to tell if your submitted patches have any meat to them.
The best way to get a job in kernel development is to spend some spare time (or get a professor to give you credit/grants for) hacking on the Linux kernel. If you'd like to try that, see the getting started in kernel hacking page.
The best way to get a job as a Linux kernel developer is to network with other Linux professionals. Try attending your local open source user groups, even if they aren't Linux specific. Go to Linux and open source conferences, and stay after talks to ask the presenters questions. This gives you an opportunity to talk to developers as you walk out of the room, and meet any of their co-workers in the hallway after wards.
Once you learn about a particular open source project or kernel subsystem, start giving talks about it, first at local user or student groups, and then at open source conferences. Being a presenter allows you to more easily network with other presenters, and builds up your credibility.
Work on other open source projects
It's useful to work on other open source projects in your spare time. If you feel you can't contribute to the kernel yet, you can still work on personal projects and publish them on github or sourceforge. That way, future employers can see your coding style, how meticuluous your code is, and how you debug and fix bugs. It also shows incentive on your part to dive into a new area you're unfamiliar with.
If you're a student, ask your professors if they have Linux or open source projects you can work on. You may be able to get paid for working on those projects, or get course credit. Those projects give you something to put on your resume when you apply for jobs. Applying to Google Summer of Code is also a good idea, even if it's not for a Linux kernel project.
Get a degree
Unfortunately, many of the top Linux employers will not hire you unless you have a four-year degree. It's most helpful to have a degree in Computer Science or Computer Engineering, but other engineering fields may also be accepted. You may be able to get consulting jobs, or a part-time job without a degree, but it's very hard to get a full-time Linux kernel job without a degree.