I'm sorry I don't know anything about patching kernels, and I'm pretty sure it's done before installation, but to install the kernel do this:
1. Unzip the Kernel archive (linux-2.6.15.tar.bz2)
2. Move the folder (linux-2.6.15) to /usr/src/kernels (If you have the kernel-devel package installed you should see the folder of the old kernel)
3. Enter the folder in a root terminal and execute the following command:
[root@whateverhost linux-2.6.15]# make xconfig
You'll get a graphical interface for choosing kernel modules and drivers. With this you choose what hardware to support, or to remove support for different things (you'll find lots of internet sources for this). WARNING: Don't do anything you're unsure of here.
When you're done, do the following:
[root@whateverhost linux-2.6.15]# make bzImage && make modules_install && make install
This should take quite a while. If all goes well and no errors occur, simply reboot and you should find the new kernel as an option in grub. It's done automatically. If anything goes wrong (Kernel panic or whatever), you can reboot into the old kernel at any time for troubleshooting.