There's not much fun in just recompiling a kernel. You invoke some script, magic happens, compile output rolls over your screen, and *ding*, you have a kernel.
In the case of the Linux kernel in particular, something like this:
make menuconfig # shows a menu where you can configure thousands of kernel options
make # do the compiling
It's not very interesting, but that's the place to start. Fiddling with the kernel options, and actually booting into your own, unique, home-baked kernel, that's where the real fun begins.
If you want to learn more about the compilation process itself, study the provided Makefile. In-depth knowledge about GNU make syntax will be helpful.
On the other end of the spectrum, there's doing everything by hand: invoking gcc for each source file, passing in the right compiler options. You would just be replicating the steps that the Makefile is doing for you. That is a nightmare, and not very educational either.