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1) cd /usr/src
2) unlink linux
3) rm -rfv linux-oldversion
4) wget http://kernel.org/pub/linux/kernel/v2.6/li...version.tar.bz2 (see www.kernel.org)
5) tar -jxvf linux-newversion.tar.bz2
6) ln -s linux-newversion linux
7) cd linux
8) make mrproper
9) make oldconfig (you may have to select new options available that wasn't on the old kernel. Generally, you're safe to just keep presseing enter for it to select the default for those new options.)
10) make menuconfig (ONLY if you want to edit kernel configuration)
11) make (go make some coffee)
12) make modules_install
13) make install
14) cp /usr/src/linux/.config /boot/config-newversion (newversion=version of the new kernel)
15) grub (you'll be enterred into a "grub>" prompt)
16) savedefault --default=0 --once
17) quit (you'll go back to normal bash prompt)
18) reboot

If the kernel boots up successfully:
1) open up /boot/grub/grub.conf in text editor
2) change "default=1" to "default=0"
3) save

If the kernel does not boot:
1) have techs simply hardboot the server letting it boot the default kernel (the old one)
2) figure out what went wrong and try again

To remove and old version of a kernel (do NOT do this for the rpm installed kernels (yum/up2date):
1) cd /boot
2)rm -fv config-oldversion initrd-oldversion System.map-oldversion vmlinuz-oldversion
3) cd /lib/modules
4) rm -rfv oldversion
5) remove entry from /boot/grub/grub.conf

Generally, when I go and delete a kernel, I leave atleast 2 installed. One older one (the previous working one) and the latest one installed. Anything older than those 2 can be removed.