Strictly, Linux is
the kernel (along with its associated modules) --- but this on its own isn't much use. This is why it's bundled with plenty of systems & application software (the things that actually enable users to do things). Such a bundle is referred to as a "distribution" (or "distro" for short). The emphasis of the distribution determines the selection of software bundled with it.
A few of the most popular distributions are Ubuntu, Fedora, SuSE, Debian (from which Ubuntu is derived) and Slackware. If you go and have a little read about these (for example on this website
), you can decide which one best suits your needs, download it (for free) and burn it onto a CD or DVD.
You then just reboot with the CD/DVD you've burned and the installation will begin. The installation process is fairly straightforward, and as a previous poster said, you don't need to worry too much about the kernel --- the most popular distributions will install a kernel for you during the installation.
Anyway, welcome to Linux and thanks for your question: it made me smile --- your asking whether one needs to install a kernel in order to run Linux made me want to reply breezily, "No, not at all, I've been running Linux for years without a kernel!". ...But then I am rather a silly sausage.